OEIS Similars: A247453, A109449
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A109449 | 1 -1 1 1 -2 1 -2 3 -3 1 5 -8 6 -4 1 -16 25 -20 10 -5 1 61 -96 75 -40 15 -6 1 -272 427 -336 175 -70 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A363394 | 1 1 -1 1 -2 1 1 -3 3 -2 1 -4 6 -8 5 1 -5 10 -20 25 -16 1 -6 15 -40 75 -96 61 1 -7 21 -70 175 -336 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A109449 | 1 1 1 1 2 1 2 3 3 1 5 8 6 4 1 16 25 20 10 5 1 61 96 75 40 15 6 1 272 427 336 175 70 21 7 1 1385 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A363394 | 1 1 1 1 2 1 1 3 3 2 1 4 6 8 5 1 5 10 20 25 16 1 6 15 40 75 96 61 1 7 21 70 175 336 427 272 1 8 28 |
| Std | Accsee docs | missing | 1 -1 0 1 -1 0 -2 1 -2 -1 5 -3 3 -1 0 -16 9 -11 -1 -6 -5 61 -35 40 0 15 9 10 -272 155 -181 -6 -76 |
| Std | AccRevsee docs | missing | 1 1 0 1 -1 0 1 -2 1 -1 1 -3 3 -5 0 1 -4 6 -14 11 -5 1 -5 10 -30 45 -51 10 1 -6 15 -55 120 -216 211 |
| Std | AntiDiagsee docs | missing | 1 -1 1 1 -2 -2 5 3 1 -16 -8 -3 61 25 6 1 -272 -96 -20 -4 1385 427 75 10 1 -7936 -2176 -336 -40 -5 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -4 3 -2 6 -9 4 5 -16 18 -16 5 -16 50 -60 40 -25 6 61 -192 225 -160 75 -36 7 -272 854 -1008 |
| Std | RowSum∑ k=0..n T(n, k) | A062162 | 1 0 0 -1 0 -5 10 -61 280 -1665 10470 -73621 561660 -4650425 41441530 -395757181 4031082640 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A062272 | 1 -1 2 -5 12 -41 152 -685 3472 -19921 126752 -887765 6781632 -56126201 500231552 -4776869245 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A062161 | 0 1 -2 4 -12 36 -142 624 -3192 18256 -116282 814144 -6219972 51475776 -458790022 4381112064 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000667 | 1 -2 4 -9 24 -77 294 -1309 6664 -38177 243034 -1701909 13001604 -107601977 959021574 -9157981309 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A343845 | 1 -1 2 -4 9 -27 93 -392 1898 -10493 64885 -443916 3326317 -27085015 238073306 -2246348560 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 0 -4 4 -30 100 -558 3008 -19170 131820 -998622 8185032 -72407530 686728900 -6953737846 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A337443 | 1 1 0 -1 -4 -5 -20 9 -208 855 -6180 41549 -321792 2651155 -23664420 225865769 -2301032256 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 120 400 146400 8710800 6434377600 718076540160 362779448854233600 919162196913676531200 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | A065619 | 1 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Std | ColMiddleT(n, n // 2) | missing | 1 -1 -2 3 6 -20 -40 175 350 -2016 -4032 28182 56364 -466752 -933504 8912475 17824950 -192924160 |
| Std | CentralET(2 n, n) | A343846 | 1 -2 6 -40 350 -4032 56364 -933504 17824950 -385848320 9334057876 -249576198144 7308698191340 |
| Std | CentralOT(2 n + 1, n) | missing | -1 3 -20 175 -2016 28182 -466752 8912475 -192924160 4667028938 -124788099072 3654349095670 |
| Std | ColLeftT(n, 0) | A000111 | 1 -1 1 -2 5 -16 61 -272 1385 -7936 50521 -353792 2702765 -22368256 199360981 -1903757312 |
| Std | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -2 -1 -6 -15 0 -271 574 -5379 12408 -63391 -355740 5907811 -87791964 971243909 -10733095626 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 6 21 90 467 2824 19383 148414 1251935 11523136 114837943 1231239108 14124972773 172584011500 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 0 -4 0 -30 70 -488 2520 -16650 115170 -883452 7301580 -65105950 621622950 -6332114896 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A337443 | 1 1 0 -1 -4 -5 -20 9 -208 855 -6180 41549 -321792 2651155 -23664420 225865769 -2301032256 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 0 -4 -20 -30 -140 72 -1872 8550 -67980 498588 -4183296 37116170 -354966300 3613852304 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A343843 | 1 -1 1 -9 33 -241 1761 -15929 161473 -1853281 23584321 -330371049 5047404513 -83546832721 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000834 | 1 3 9 35 177 1123 8569 76355 777697 8911683 113466729 1589173475 24280777617 401898209443 |
| Std | DiagRow1T(n + 1, n) | A000027 | -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 |
| Std | DiagRow2T(n + 2, n) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Std | DiagRow3T(n + 3, n) | A007290 | -2 -8 -20 -40 -70 -112 -168 -240 -330 -440 -572 -728 -910 -1120 -1360 -1632 -1938 -2280 -2660 -3080 |
| Std | DiagCol1T(n + 1, 1) | A065619 | 1 -2 3 -8 25 -96 427 -2176 12465 -79360 555731 -4245504 35135945 -313155584 2990414715 -30460116992 |
| Std | DiagCol2T(n + 2, 2) | A162171 | 1 -3 6 -20 75 -336 1708 -9792 62325 -436480 3334386 -27595776 245951615 -2348666880 23923317720 |
| Std | DiagCol3T(n + 3, 3) | missing | 1 -4 10 -40 175 -896 5124 -32640 228525 -1745920 14449006 -128780288 1229758075 -12526223360 |
| Std | Polysee docs | missing | 1 -1 1 1 0 1 -2 0 1 1 5 -1 1 2 1 -16 0 0 4 3 1 61 -5 -3 7 9 4 1 -272 10 -14 8 26 16 5 1 1385 -61 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A068601 | -2 -1 0 7 26 63 124 215 342 511 728 999 1330 1727 2196 2743 3374 4095 4912 5831 6858 7999 9260 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A102590 | 1 1 1 0 -3 -14 -39 -130 -263 -1214 -179 -21810 98277 -1021214 8446881 -82814290 836117617 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 4 7 8 -13 -146 -773 -3352 -13633 -52046 -202253 -724012 -3012553 -8839346 -57776933 15860528 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 1 7 69 859 12985 231155 4738153 109925183 2847749421 81488820579 2552715369677 86889633786487 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A109449 | 1 -1 -1 1 2 1 -2 -3 -3 -1 5 8 6 4 1 -16 -25 -20 -10 -5 -1 61 96 75 40 15 6 1 -272 -427 -336 -175 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A363394 | 1 -1 -1 1 2 1 -1 -3 -3 -2 1 4 6 8 5 -1 -5 -10 -20 -25 -16 1 6 15 40 75 96 61 -1 -7 -21 -70 -175 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 1 1 -3 -2 1 -4 -3 3 1 21 16 -18 -4 1 46 35 -40 -10 5 1 -363 -276 315 80 -45 -6 1 -1114 -847 966 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 -2 -3 1 3 -3 -4 1 -4 -18 16 21 1 5 -10 -40 35 46 1 -6 -45 80 315 -276 -363 1 7 -21 -140 245 |
| Alt | Accsee docs | missing | 1 -1 -2 1 3 4 -2 -5 -8 -9 5 13 19 23 24 -16 -41 -61 -71 -76 -77 61 157 232 272 287 293 294 -272 |
| Alt | AccRevsee docs | missing | 1 -1 -2 1 3 4 -1 -4 -7 -9 1 5 11 19 24 -1 -6 -16 -36 -61 -77 1 7 22 62 137 233 294 -1 -8 -29 -99 |
| Alt | AntiDiagsee docs | missing | 1 -1 1 -1 -2 2 5 -3 1 -16 8 -3 61 -25 6 -1 -272 96 -20 4 1385 -427 75 -10 1 -7936 2176 -336 40 -5 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 -1 -2 1 4 3 -2 -6 -9 -4 5 16 18 16 5 -16 -50 -60 -40 -25 -6 61 192 225 160 75 36 7 -272 -854 |
| Alt | RowSum∑ k=0..n T(n, k) | A000667 | 1 -2 4 -9 24 -77 294 -1309 6664 -38177 243034 -1701909 13001604 -107601977 959021574 -9157981309 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A062272 | 1 -1 2 -5 12 -41 152 -685 3472 -19921 126752 -887765 6781632 -56126201 500231552 -4776869245 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A062161 | 0 -1 2 -4 12 -36 142 -624 3192 -18256 116282 -814144 6219972 -51475776 458790022 -4381112064 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A062162 | 1 0 0 -1 0 -5 10 -61 280 -1665 10470 -73621 561660 -4650425 41441530 -395757181 4031082640 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 0 0 3 -11 41 -192 1024 -6061 39603 -283392 2204565 -18528503 167343104 -1616537472 16633258447 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -3 8 -24 84 -342 1596 -8414 49504 -321794 2291604 -17749534 148597944 -1337406826 12878895932 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000737 | 1 -3 8 -21 60 -197 756 -3367 17136 -98153 624804 -4375283 33424512 -276622829 2465449252 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 120 400 146400 8710800 6434377600 718076540160 362779448854233600 919162196913676531200 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A065619 | 1 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 -1 2 -3 6 -20 40 -175 350 -2016 4032 -28182 56364 -466752 933504 -8912475 17824950 -192924160 |
| Alt | CentralET(2 n, n) | A343846 | 1 2 6 40 350 4032 56364 933504 17824950 385848320 9334057876 249576198144 7308698191340 |
| Alt | CentralOT(2 n + 1, n) | missing | -1 -3 -20 -175 -2016 -28182 -466752 -8912475 -192924160 -4667028938 -124788099072 -3654349095670 |
| Alt | ColLeftT(n, 0) | A000111 | 1 -1 1 -2 5 -16 61 -272 1385 -7936 50521 -353792 2702765 -22368256 199360981 -1903757312 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -2 6 -21 90 -467 2824 -19383 148414 -1251935 11523136 -114837943 1231239108 -14124972773 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -2 1 -6 15 0 271 574 5379 12408 63391 -355740 -5907811 -87791964 -971243909 -10733095626 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A231179 | 0 -1 4 -12 36 -120 462 -2058 10472 -59976 381770 -2673374 20422908 -169020852 1506427678 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000737 | 1 -3 8 -21 60 -197 756 -3367 17136 -98153 624804 -4375283 33424512 -276622829 2465449252 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 6 -24 84 -300 1182 -5292 26936 -154224 981530 -6872844 52503396 -434518656 3872719606 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000834 | 1 -3 9 -35 177 -1123 8569 -76355 777697 -8911683 113466729 -1589173475 24280777617 -401898209443 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A343843 | 1 1 1 9 33 241 1761 15929 161473 1853281 23584321 330371049 5047404513 83546832721 1489242229281 |
| Alt | DiagRow1T(n + 1, n) | A000027 | -1 2 -3 4 -5 6 -7 8 -9 10 -11 12 -13 14 -15 16 -17 18 -19 20 -21 22 -23 24 -25 26 -27 28 -29 30 -31 |
| Alt | DiagRow2T(n + 2, n) | A000217 | 1 -3 6 -10 15 -21 28 -36 45 -55 66 -78 91 -105 120 -136 153 -171 190 -210 231 -253 276 -300 325 |
| Alt | DiagRow3T(n + 3, n) | A007290 | -2 8 -20 40 -70 112 -168 240 -330 440 -572 728 -910 1120 -1360 1632 -1938 2280 -2660 3080 -3542 |
| Alt | DiagCol1T(n + 1, 1) | A065619 | -1 2 -3 8 -25 96 -427 2176 -12465 79360 -555731 4245504 -35135945 313155584 -2990414715 30460116992 |
| Alt | DiagCol2T(n + 2, 2) | A162171 | 1 -3 6 -20 75 -336 1708 -9792 62325 -436480 3334386 -27595776 245951615 -2348666880 23923317720 |
| Alt | DiagCol3T(n + 3, 3) | missing | -1 4 -10 40 -175 896 -5124 32640 -228525 1745920 -14449006 128780288 -1229758075 12526223360 |
| Alt | Polysee docs | missing | 1 -1 1 1 -2 1 -2 4 -3 1 5 -9 9 -4 1 -16 24 -28 16 -5 1 61 -77 93 -65 25 -6 1 -272 294 -338 272 -126 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A001093 | -2 -9 -28 -65 -126 -217 -344 -513 -730 -1001 -1332 -1729 -2198 -2745 -3376 -4097 -4914 -5833 -6860 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A000752 | 1 -3 9 -28 93 -338 1369 -6238 31993 -183618 1169229 -8187598 62545893 -517622498 4613366689 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A307878 | 1 -4 16 -65 272 -1189 5506 -27365 147512 -868129 5589646 -39309965 300724652 -2489776969 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A292976 | 1 -2 9 -65 645 -8141 124729 -2247853 46584937 -1091386465 28521016621 -822514469149 25946988879053 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A363394 | 1 1 -1 1 -2 1 1 -3 3 -2 1 -4 6 -8 5 1 -5 10 -20 25 -16 1 -6 15 -40 75 -96 61 1 -7 21 -70 175 -336 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A109449 | 1 1 1 1 2 1 2 3 3 1 5 8 6 4 1 16 25 20 10 5 1 61 96 75 40 15 6 1 272 427 336 175 70 21 7 1 1385 |
| Rev | Accsee docs | missing | 1 1 0 1 -1 0 1 -2 1 -1 1 -3 3 -5 0 1 -4 6 -14 11 -5 1 -5 10 -30 45 -51 10 1 -6 15 -55 120 -216 211 |
| Rev | AccRevsee docs | missing | 1 -1 0 1 -1 0 -2 1 -2 -1 5 -3 3 -1 0 -16 9 -11 -1 -6 -5 61 -35 40 0 15 9 10 -272 155 -181 -6 -76 |
| Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 1 1 -4 3 1 -5 6 -2 1 -6 10 -8 1 -7 15 -20 5 1 -8 21 -40 25 1 -9 28 -70 75 -16 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -4 3 1 -6 9 -8 1 -8 18 -32 25 1 -10 30 -80 125 -96 1 -12 45 -160 375 -576 427 1 -14 63 |
| Rev | RowSum∑ k=0..n T(n, k) | A062162 | 1 0 0 -1 0 -5 10 -61 280 -1665 10470 -73621 561660 -4650425 41441530 -395757181 4031082640 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A003701 | 1 1 2 4 12 36 152 624 3472 18256 126752 814144 6781632 51475776 500231552 4381112064 48656756992 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A009739 | 0 -1 -2 -5 -12 -41 -142 -685 -3192 -19921 -116282 -887765 -6219972 -56126201 -458790022 -4776869245 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -1 -1 0 0 -3 -6 -1 9 -6 -58 -35 194 191 -1009 -1728 4600 12209 -24126 -95361 118201 751562 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A337443 | 1 1 0 -1 -4 -5 -20 9 -208 855 -6180 41549 -321792 2651155 -23664420 225865769 -2301032256 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 0 -4 4 -30 100 -558 3008 -19170 131820 -998622 8185032 -72407530 686728900 -6953737846 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 120 400 146400 8710800 6434377600 718076540160 362779448854233600 919162196913676531200 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A065619 | 1 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -3 6 10 -40 -70 350 630 -4032 -7392 56364 104676 -933504 -1750320 17824950 33669350 |
| Rev | CentralET(2 n, n) | A343846 | 1 -2 6 -40 350 -4032 56364 -933504 17824950 -385848320 9334057876 -249576198144 7308698191340 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 -3 10 -70 630 -7392 104676 -1750320 33669350 -733111808 17819565036 -478354379776 14055188829500 |
| Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | ColRightT(n, n) | A000111 | 1 -1 1 -2 5 -16 61 -272 1385 -7936 50521 -353792 2702765 -22368256 199360981 -1903757312 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -2 -1 -6 -15 0 -271 574 -5379 12408 -63391 -355740 5907811 -87791964 971243909 -10733095626 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 6 -21 90 -467 2824 -19383 148414 -1251935 11523136 -114837943 1231239108 -14124972773 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 0 -3 4 -25 90 -497 2728 -17505 121350 -925001 7623372 -67757105 645287370 -6557980665 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 0 -4 4 -30 100 -558 3008 -19170 131820 -998622 8185032 -72407530 686728900 -6953737846 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 -9 28 -145 690 -4109 25800 -182097 1388550 -11509861 102580476 -979946201 9982622650 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A102590 | 1 1 1 0 -3 -14 -39 -130 -263 -1214 -179 -21810 98277 -1021214 8446881 -82814290 836117617 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000752 | 1 -3 9 -28 93 -338 1369 -6238 31993 -183618 1169229 -8187598 62545893 -517622498 4613366689 |
| Rev | DiagRow1T(n + 1, n) | A065619 | 1 -2 3 -8 25 -96 427 -2176 12465 -79360 555731 -4245504 35135945 -313155584 2990414715 -30460116992 |
| Rev | DiagRow2T(n + 2, n) | A162171 | 1 -3 6 -20 75 -336 1708 -9792 62325 -436480 3334386 -27595776 245951615 -2348666880 23923317720 |
| Rev | DiagRow3T(n + 3, n) | missing | 1 -4 10 -40 175 -896 5124 -32640 228525 -1745920 14449006 -128780288 1229758075 -12526223360 |
| Rev | DiagCol1T(n + 1, 1) | A000027 | -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 |
| Rev | DiagCol2T(n + 2, 2) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Rev | DiagCol3T(n + 3, 3) | A007290 | -2 -8 -20 -40 -70 -112 -168 -240 -330 -440 -572 -728 -910 -1120 -1360 -1632 -1938 -2280 -2660 -3080 |
| Rev | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 -1 1 -2 1 1 0 -9 4 -3 1 1 -5 33 -35 9 -4 1 1 10 -241 232 -91 16 -5 1 1 -61 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A005898 | 1 -1 -9 -35 -91 -189 -341 -559 -855 -1241 -1729 -2331 -3059 -3925 -4941 -6119 -7471 -9009 -10745 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A343843 | 1 -1 1 -9 33 -241 1761 -15929 161473 -1853281 23584321 -330371049 5047404513 -83546832721 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 4 -35 232 -2327 26254 -352775 5381032 -92544227 1767139954 -37127146415 850874177332 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 1 -35 849 -36649 2188585 -179017579 19092801217 -2582218381193 431768517064401 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A109449 | 1 1 1 1 2 1 2 3 3 1 5 8 6 4 1 16 25 20 10 5 1 61 96 75 40 15 6 1 272 427 336 175 70 21 7 1 1385 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A363394 | 1 1 1 1 2 1 1 3 3 2 1 4 6 8 5 1 5 10 20 25 16 1 6 15 40 75 96 61 1 7 21 70 175 336 427 272 1 8 28 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A363394 | 1 1 -1 1 -2 1 1 -3 3 -2 1 -4 6 -8 5 1 -5 10 -20 25 -16 1 -6 15 -40 75 -96 61 1 -7 21 -70 175 -336 |
| Inv | Accsee docs | missing | 1 1 2 1 3 4 2 5 8 9 5 13 19 23 24 16 41 61 71 76 77 61 157 232 272 287 293 294 272 699 1035 1210 |
| Inv | AccRevsee docs | missing | 1 1 2 1 3 4 1 4 7 9 1 5 11 19 24 1 6 16 36 61 77 1 7 22 62 137 233 294 1 8 29 99 274 610 1037 1309 |
| Inv | AntiDiagsee docs | missing | 1 1 1 1 2 2 5 3 1 16 8 3 61 25 6 1 272 96 20 4 1385 427 75 10 1 7936 2176 336 40 5 50521 12465 1708 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 3 2 6 9 4 5 16 18 16 5 16 50 60 40 25 6 61 192 225 160 75 36 7 272 854 1008 700 350 126 |
| Inv | RowSum∑ k=0..n T(n, k) | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A062272 | 1 1 2 5 12 41 152 685 3472 19921 126752 887765 6781632 56126201 500231552 4776869245 48656756992 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A062161 | 0 1 2 4 12 36 142 624 3192 18256 116282 814144 6219972 51475776 458790022 4381112064 44625674352 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A062162 | 1 0 0 1 0 5 10 61 280 1665 10470 73621 561660 4650425 41441530 395757181 4031082640 43626778785 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A343845 | 1 1 2 4 9 27 93 392 1898 10493 64885 443916 3326317 27085015 238073306 2246348560 22643042325 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 8 24 84 342 1596 8414 49504 321794 2291604 17749534 148597944 1337406826 12878895932 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000737 | 1 3 8 21 60 197 756 3367 17136 98153 624804 4375283 33424512 276622829 2465449252 23543304919 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 120 400 146400 8710800 6434377600 718076540160 362779448854233600 919162196913676531200 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | A065619 | 1 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 1 2 3 6 20 40 175 350 2016 4032 28182 56364 466752 933504 8912475 17824950 192924160 385848320 |
| Inv | CentralET(2 n, n) | A343846 | 1 2 6 40 350 4032 56364 933504 17824950 385848320 9334057876 249576198144 7308698191340 |
| Inv | CentralOT(2 n + 1, n) | missing | 1 3 20 175 2016 28182 466752 8912475 192924160 4667028938 124788099072 3654349095670 |
| Inv | ColLeftT(n, 0) | A000111 | 1 1 1 2 5 16 61 272 1385 7936 50521 353792 2702765 22368256 199360981 1903757312 19391512145 |
| Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 6 21 90 467 2824 19383 148414 1251935 11523136 114837943 1231239108 14124972773 172584011500 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -2 -1 -6 -15 0 -271 574 -5379 12408 -63391 -355740 5907811 -87791964 971243909 -10733095626 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A231179 | 0 1 4 12 36 120 462 2058 10472 59976 381770 2673374 20422908 169020852 1506427678 14385323610 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A000737 | 1 3 8 21 60 197 756 3367 17136 98153 624804 4375283 33424512 276622829 2465449252 23543304919 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 24 84 300 1182 5292 26936 154224 981530 6872844 52503396 434518656 3872719606 36981738780 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000834 | 1 3 9 35 177 1123 8569 76355 777697 8911683 113466729 1589173475 24280777617 401898209443 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A343843 | 1 -1 1 -9 33 -241 1761 -15929 161473 -1853281 23584321 -330371049 5047404513 -83546832721 |
| Inv | DiagRow1T(n + 1, n) | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Inv | DiagRow2T(n + 2, n) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Inv | DiagRow3T(n + 3, n) | A007290 | 2 8 20 40 70 112 168 240 330 440 572 728 910 1120 1360 1632 1938 2280 2660 3080 3542 4048 4600 5200 |
| Inv | DiagCol1T(n + 1, 1) | A065619 | 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Inv | DiagCol2T(n + 2, 2) | A162171 | 1 3 6 20 75 336 1708 9792 62325 436480 3334386 27595776 245951615 2348666880 23923317720 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 4 10 40 175 896 5124 32640 228525 1745920 14449006 128780288 1229758075 12526223360 135565467080 |
| Inv | Polysee docs | missing | 1 1 1 1 2 1 2 4 3 1 5 9 9 4 1 16 24 28 16 5 1 61 77 93 65 25 6 1 272 294 338 272 126 36 7 1 1385 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A001093 | 2 9 28 65 126 217 344 513 730 1001 1332 1729 2198 2745 3376 4097 4914 5833 6860 8001 9262 10649 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A000752 | 1 3 9 28 93 338 1369 6238 31993 183618 1169229 8187598 62545893 517622498 4613366689 44054301358 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | A307878 | 1 4 16 65 272 1189 5506 27365 147512 868129 5589646 39309965 300724652 2489776969 22192420786 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A292976 | 1 2 9 65 645 8141 124729 2247853 46584937 1091386465 28521016621 822514469149 25946988879053 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A363394 | 1 1 1 1 2 1 1 3 3 2 1 4 6 8 5 1 5 10 20 25 16 1 6 15 40 75 96 61 1 7 21 70 175 336 427 272 1 8 28 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A109449 | 1 1 1 1 2 1 2 3 3 1 5 8 6 4 1 16 25 20 10 5 1 61 96 75 40 15 6 1 272 427 336 175 70 21 7 1 1385 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A109449 | 1 -1 1 1 -2 1 -2 3 -3 1 5 -8 6 -4 1 -16 25 -20 10 -5 1 61 -96 75 -40 15 -6 1 -272 427 -336 175 -70 |
| Inv:Rev | Accsee docs | missing | 1 1 2 1 3 4 1 4 7 9 1 5 11 19 24 1 6 16 36 61 77 1 7 22 62 137 233 294 1 8 29 99 274 610 1037 1309 |
| Inv:Rev | AccRevsee docs | missing | 1 1 2 1 3 4 2 5 8 9 5 13 19 23 24 16 41 61 71 76 77 61 157 232 272 287 293 294 272 699 1035 1210 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 1 1 4 3 1 5 6 2 1 6 10 8 1 7 15 20 5 1 8 21 40 25 1 9 28 70 75 16 1 10 36 112 175 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 3 1 6 9 8 1 8 18 32 25 1 10 30 80 125 96 1 12 45 160 375 576 427 1 14 63 280 875 2016 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A003701 | 1 1 2 4 12 36 152 624 3472 18256 126752 814144 6781632 51475776 500231552 4381112064 48656756992 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A009739 | 0 1 2 5 12 41 142 685 3192 19921 116282 887765 6219972 56126201 458790022 4776869245 44625674352 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A062162 | 1 0 0 -1 0 -5 10 -61 280 -1665 10470 -73621 561660 -4650425 41441530 -395757181 4031082640 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000667 | 1 2 4 9 24 77 294 1309 6664 38177 243034 1701909 13001604 107601977 959021574 9157981309 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 3 5 8 14 25 48 95 199 430 972 2261 5456 13515 34533 90384 243030 668117 1881192 5406567 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000737 | 1 3 8 21 60 197 756 3367 17136 98153 624804 4375283 33424512 276622829 2465449252 23543304919 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 8 24 84 342 1596 8414 49504 321794 2291604 17749534 148597944 1337406826 12878895932 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 120 400 146400 8710800 6434377600 718076540160 362779448854233600 919162196913676531200 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | A065619 | 1 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 3 6 10 40 70 350 630 4032 7392 56364 104676 933504 1750320 17824950 33669350 385848320 |
| Inv:Rev | CentralET(2 n, n) | A343846 | 1 2 6 40 350 4032 56364 933504 17824950 385848320 9334057876 249576198144 7308698191340 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 3 10 70 630 7392 104676 1750320 33669350 733111808 17819565036 478354379776 14055188829500 |
| Inv:Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | ColRightT(n, n) | A000111 | 1 1 1 2 5 16 61 272 1385 7936 50521 353792 2702765 22368256 199360981 1903757312 19391512145 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 6 21 90 467 2824 19383 148414 1251935 11523136 114837943 1231239108 14124972773 172584011500 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -2 1 -6 15 0 271 574 5379 12408 63391 -355740 -5907811 -87791964 -971243909 -10733095626 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 4 15 60 265 1302 7105 42840 283617 2048570 16047625 135596340 1229804849 11919874358 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 8 24 84 342 1596 8414 49504 321794 2291604 17749534 148597944 1337406826 12878895932 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 33 180 1025 6222 40621 285880 2166993 17649530 153989605 1434584580 14224710617 149660973126 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000752 | 1 3 9 28 93 338 1369 6238 31993 183618 1169229 8187598 62545893 517622498 4613366689 44054301358 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A102590 | 1 -1 1 0 -3 14 -39 130 -263 1214 -179 21810 98277 1021214 8446881 82814290 836117617 9075846014 |
| Inv:Rev | DiagRow1T(n + 1, n) | A065619 | 1 2 3 8 25 96 427 2176 12465 79360 555731 4245504 35135945 313155584 2990414715 30460116992 |
| Inv:Rev | DiagRow2T(n + 2, n) | A162171 | 1 3 6 20 75 336 1708 9792 62325 436480 3334386 27595776 245951615 2348666880 23923317720 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 4 10 40 175 896 5124 32640 228525 1745920 14449006 128780288 1229758075 12526223360 135565467080 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A007290 | 2 8 20 40 70 112 168 240 330 440 572 728 910 1120 1360 1632 1938 2280 2660 3080 3542 4048 4600 5200 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 2 1 1 4 3 1 1 9 9 4 1 1 24 35 16 5 1 1 77 177 91 25 6 1 1 294 1123 688 189 36 7 1 1 1309 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A005898 | 1 9 35 91 189 341 559 855 1241 1729 2331 3059 3925 4941 6119 7471 9009 10745 12691 14859 17261 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A000834 | 1 3 9 35 177 1123 8569 76355 777697 8911683 113466729 1589173475 24280777617 401898209443 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 16 91 688 6559 75106 1004071 15340408 263683459 5035965646 105797928751 2424709105228 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 9 91 1905 68401 3698929 280332235 28278441793 3660827615785 591142123944601 116435201160887159 |
| << | Table | Source | Similars | Index | >> |
Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.