OEIS Similars: A038207
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A038207 | 1 2 1 4 4 1 8 12 6 1 16 32 24 8 1 32 80 80 40 10 1 64 192 240 160 60 12 1 128 448 672 560 280 84 14 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A013609 | 1 1 2 1 4 4 1 6 12 8 1 8 24 32 16 1 10 40 80 80 32 1 12 60 160 240 192 64 1 14 84 280 560 672 448 |
| Std | Accsee docs | missing | 1 2 3 4 8 9 8 20 26 27 16 48 72 80 81 32 112 192 232 242 243 64 256 496 656 716 728 729 128 576 |
| Std | AccRevsee docs | missing | 1 1 3 1 5 9 1 7 19 27 1 9 33 65 81 1 11 51 131 211 243 1 13 73 233 473 665 729 1 15 99 379 939 1611 |
| Std | AntiDiagsee docs | A207538 | 1 2 4 1 8 4 16 12 1 32 32 6 64 80 24 1 128 192 80 8 256 448 240 40 1 512 1024 672 160 10 1024 2304 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 2 2 4 8 3 8 24 18 4 16 64 72 32 5 32 160 240 160 50 6 64 384 720 640 300 72 7 128 896 2016 2240 |
| Std | RowSum∑ k=0..n T(n, k) | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A007051 | 1 2 5 14 41 122 365 1094 3281 9842 29525 88574 265721 797162 2391485 7174454 21523361 64570082 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A003462 | 0 1 4 13 40 121 364 1093 3280 9841 29524 88573 265720 797161 2391484 7174453 21523360 64570081 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | 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 | AbsSum∑ k=0..n | T(n, k) | | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A000129 | 1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A081038 | 1 5 21 81 297 1053 3645 12393 41553 137781 452709 1476225 4782969 15411789 49424013 157837977 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A006234 | 1 4 15 54 189 648 2187 7290 24057 78732 255879 826686 2657205 8503056 27103491 86093442 272629233 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 4 24 96 160 960 13440 35840 32256 322560 2365440 28385280 52715520 49201152 1476034560 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A171977 | 1 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 32 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 64 2 4 2 8 2 4 2 16 2 4 2 8 2 4 |
| Std | RowMaxMax k=0..n | T(n, k) | | A109388 | 1 2 4 12 32 80 240 672 1792 5376 15360 42240 126720 366080 1025024 3075072 8945664 25346048 |
| Std | ColMiddleT(n, n // 2) | missing | 1 2 4 12 24 80 160 560 1120 4032 8064 29568 59136 219648 439296 1647360 3294720 12446720 24893440 |
| Std | CentralET(2 n, n) | A059304 | 1 4 24 160 1120 8064 59136 439296 3294720 24893440 189190144 1444724736 11076222976 85201715200 |
| Std | CentralOT(2 n + 1, n) | A069723 | 2 12 80 560 4032 29568 219648 1647360 12446720 94595072 722362368 5538111488 42600857600 |
| Std | ColLeftT(n, 0) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| 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) | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A098332 | 1 -1 -3 11 1 -81 141 363 -1791 479 13597 -29877 -54911 353807 -223443 -2539989 6806529 8302527 |
| Std | TransNat0∑ k=0..n T(n, k) k | A027471 | 0 1 6 27 108 405 1458 5103 17496 59049 196830 649539 2125764 6908733 22320522 71744535 229582512 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A006234 | 1 4 15 54 189 648 2187 7290 24057 78732 255879 826686 2657205 8503056 27103491 86093442 272629233 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 8 45 216 945 3888 15309 58320 216513 787320 2814669 9920232 34543665 119042784 406552365 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000351 | 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Std | DiagRow1T(n + 1, n) | A005843 | 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Std | DiagRow2T(n + 2, n) | A046092 | 4 12 24 40 60 84 112 144 180 220 264 312 364 420 480 544 612 684 760 840 924 1012 1104 1200 1300 |
| Std | DiagRow3T(n + 3, n) | A130809 | 8 32 80 160 280 448 672 960 1320 1760 2288 2912 3640 4480 5440 6528 7752 9120 10640 12320 14168 |
| Std | DiagCol1T(n + 1, 1) | A001787 | 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 4980736 |
| Std | DiagCol2T(n + 2, 2) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Std | DiagCol3T(n + 3, 3) | A001789 | 1 8 40 160 560 1792 5376 15360 42240 112640 292864 745472 1863680 4587520 11141120 26738688 |
| Std | Polysee docs | A051129 | 1 2 1 4 3 1 8 9 4 1 16 27 16 5 1 32 81 64 25 6 1 64 243 256 125 36 7 1 128 729 1024 625 216 49 8 1 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 37 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 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 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 10648 12167 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A000302 | 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A000351 | 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A000272 | 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 56693912375296 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A038207 | 1 2 -1 4 -4 1 8 -12 6 -1 16 -32 24 -8 1 32 -80 80 -40 10 -1 64 -192 240 -160 60 -12 1 128 -448 672 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A013609 | 1 -1 2 1 -4 4 -1 6 -12 8 1 -8 24 -32 16 -1 10 -40 80 -80 32 1 -12 60 -160 240 -192 64 -1 14 -84 280 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -2 1 -12 4 1 40 -12 -6 1 528 -160 -72 8 1 -2912 880 400 -40 -10 1 -57792 17472 7920 -800 -180 12 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -2 1 4 -12 1 -6 -12 40 1 8 -72 -160 528 1 -10 -40 400 880 -2912 1 12 -180 -800 7920 17472 |
| Alt | Accsee docs | missing | 1 2 1 4 0 1 8 -4 2 1 16 -16 8 0 1 32 -48 32 -8 2 1 64 -128 112 -48 12 0 1 128 -320 352 -208 72 -12 |
| Alt | AccRevsee docs | A119258 | 1 -1 1 1 -3 1 -1 5 -7 1 1 -7 17 -15 1 -1 9 -31 49 -31 1 1 -11 49 -111 129 -63 1 -1 13 -71 209 -351 |
| Alt | AntiDiagsee docs | A207538 | 1 2 4 -1 8 -4 16 -12 1 32 -32 6 64 -80 24 -1 128 -192 80 -8 256 -448 240 -40 1 512 -1024 672 -160 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 2 -2 4 -8 3 8 -24 18 -4 16 -64 72 -32 5 32 -160 240 -160 50 -6 64 -384 720 -640 300 -72 7 128 |
| Alt | RowSum∑ k=0..n T(n, k) | 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 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A007051 | 1 2 5 14 41 122 365 1094 3281 9842 29525 88574 265721 797162 2391485 7174454 21523361 64570082 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A003462 | 0 -1 -4 -13 -40 -121 -364 -1093 -3280 -9841 -29524 -88573 -265720 -797161 -2391484 -7174453 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, 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 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | 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 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 4 24 96 160 960 13440 35840 32256 322560 2365440 28385280 52715520 49201152 1476034560 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A171977 | 1 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 32 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 64 2 4 2 8 2 4 2 16 2 4 2 8 2 4 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A109388 | 1 2 4 12 32 80 240 672 1792 5376 15360 42240 126720 366080 1025024 3075072 8945664 25346048 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 2 -4 -12 24 80 -160 -560 1120 4032 -8064 -29568 59136 219648 -439296 -1647360 3294720 12446720 |
| Alt | CentralET(2 n, n) | A059304 | 1 -4 24 -160 1120 -8064 59136 -439296 3294720 -24893440 189190144 -1444724736 11076222976 |
| Alt | CentralOT(2 n + 1, n) | A069723 | 2 -12 80 -560 4032 -29568 219648 -1647360 12446720 -94595072 722362368 -5538111488 42600857600 |
| Alt | ColLeftT(n, 0) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A098332 | 1 1 -3 -11 1 81 141 -363 -1791 -479 13597 29877 -54911 -353807 -223443 2539989 6806529 -8302527 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A001850 | 1 -3 13 -63 321 -1683 8989 -48639 265729 -1462563 8097453 -45046719 251595969 -1409933619 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000027 | 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 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | 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 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A005563 | 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000351 | 1 -5 25 -125 625 -3125 15625 -78125 390625 -1953125 9765625 -48828125 244140625 -1220703125 |
| Alt | DiagRow1T(n + 1, n) | A005843 | 2 -4 6 -8 10 -12 14 -16 18 -20 22 -24 26 -28 30 -32 34 -36 38 -40 42 -44 46 -48 50 -52 54 -56 58 |
| Alt | DiagRow2T(n + 2, n) | A046092 | 4 -12 24 -40 60 -84 112 -144 180 -220 264 -312 364 -420 480 -544 612 -684 760 -840 924 -1012 1104 |
| Alt | DiagRow3T(n + 3, n) | A130809 | 8 -32 80 -160 280 -448 672 -960 1320 -1760 2288 -2912 3640 -4480 5440 -6528 7752 -9120 10640 -12320 |
| Alt | DiagCol1T(n + 1, 1) | A001787 | -1 -4 -12 -32 -80 -192 -448 -1024 -2304 -5120 -11264 -24576 -53248 -114688 -245760 -524288 -1114112 |
| Alt | DiagCol2T(n + 2, 2) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Alt | DiagCol3T(n + 3, 3) | A001789 | -1 -8 -40 -160 -560 -1792 -5376 -15360 -42240 -112640 -292864 -745472 -1863680 -4587520 -11141120 |
| Alt | Polysee docs | missing | 1 2 1 4 1 1 8 1 0 1 16 1 0 -1 1 32 1 0 1 -2 1 64 1 0 -1 4 -3 1 128 1 0 1 -8 9 -4 1 256 1 0 -1 16 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 2 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 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 4 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 8 1 0 -1 -8 -27 -64 -125 -216 -343 -512 -729 -1000 -1331 -1728 -2197 -2744 -3375 -4096 -4913 -5832 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A008788 | 1 1 0 -1 16 -243 4096 -78125 1679616 -40353607 1073741824 -31381059609 1000000000000 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A013609 | 1 1 2 1 4 4 1 6 12 8 1 8 24 32 16 1 10 40 80 80 32 1 12 60 160 240 192 64 1 14 84 280 560 672 448 |
| Rev | Accsee docs | missing | 1 1 3 1 5 9 1 7 19 27 1 9 33 65 81 1 11 51 131 211 243 1 13 73 233 473 665 729 1 15 99 379 939 1611 |
| Rev | AccRevsee docs | missing | 1 2 3 4 8 9 8 20 26 27 16 48 72 80 81 32 112 192 232 242 243 64 256 496 656 716 728 729 128 576 |
| Rev | AntiDiagsee docs | A128099 | 1 1 1 2 1 4 1 6 4 1 8 12 1 10 24 8 1 12 40 32 1 14 60 80 16 1 16 84 160 80 1 18 112 280 240 32 1 20 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 4 1 8 12 1 12 36 32 1 16 72 128 80 1 20 120 320 400 192 1 24 180 640 1200 1152 448 1 28 252 |
| Rev | RowSum∑ k=0..n T(n, k) | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A046717 | 1 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453 21523361 64570081 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A152011 | 0 2 4 14 40 122 364 1094 3280 9842 29524 88574 265720 797162 2391484 7174454 21523360 64570082 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A001045 | 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381 174763 349525 699051 1398101 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A006234 | 1 4 15 54 189 648 2187 7290 24057 78732 255879 826686 2657205 8503056 27103491 86093442 272629233 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A081038 | 1 5 21 81 297 1053 3645 12393 41553 137781 452709 1476225 4782969 15411789 49424013 157837977 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 4 24 96 160 960 13440 35840 32256 322560 2365440 28385280 52715520 49201152 1476034560 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A171977 | 1 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 32 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 64 2 4 2 8 2 4 2 16 2 4 2 8 2 4 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A109388 | 1 2 4 12 32 80 240 672 1792 5376 15360 42240 126720 366080 1025024 3075072 8945664 25346048 |
| Rev | ColMiddleT(n, n // 2) | A098660 | 1 1 4 6 24 40 160 280 1120 2016 8064 14784 59136 109824 439296 823680 3294720 6223360 24893440 |
| Rev | CentralET(2 n, n) | A059304 | 1 4 24 160 1120 8064 59136 439296 3294720 24893440 189190144 1444724736 11076222976 85201715200 |
| Rev | CentralOT(2 n + 1, n) | A069720 | 1 6 40 280 2016 14784 109824 823680 6223360 47297536 361181184 2769055744 21300428800 164317593600 |
| 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) | A000079 | 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A098332 | 1 1 -3 -11 1 81 141 -363 -1791 -479 13597 29877 -54911 -353807 -223443 2539989 6806529 -8302527 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A212697 | 0 2 12 54 216 810 2916 10206 34992 118098 393660 1299078 4251528 13817466 44641044 143489070 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A081038 | 1 5 21 81 297 1053 3645 12393 41553 137781 452709 1476225 4782969 15411789 49424013 157837977 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A062189 | 0 2 20 126 648 2970 12636 51030 198288 747954 2755620 9959598 35429400 124357194 431530092 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000302 | 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev | DiagRow1T(n + 1, n) | A001787 | 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 4980736 |
| Rev | DiagRow2T(n + 2, n) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Rev | DiagRow3T(n + 3, n) | A001789 | 1 8 40 160 560 1792 5376 15360 42240 112640 292864 745472 1863680 4587520 11141120 26738688 |
| Rev | DiagCol1T(n + 1, 1) | A005843 | 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Rev | DiagCol2T(n + 2, 2) | A046092 | 4 12 24 40 60 84 112 144 180 220 264 312 364 420 480 544 612 684 760 840 924 1012 1104 1200 1300 |
| Rev | DiagCol3T(n + 3, 3) | A130809 | 8 32 80 160 280 448 672 960 1320 1760 2288 2912 3640 4480 5440 6528 7752 9120 10640 12320 14168 |
| Rev | Polysee docs | A145905 | 1 1 1 1 3 1 1 9 5 1 1 27 25 7 1 1 81 125 49 9 1 1 243 625 343 81 11 1 1 729 3125 2401 729 121 13 1 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A016754 | 1 9 25 49 81 121 169 225 289 361 441 529 625 729 841 961 1089 1225 1369 1521 1681 1849 2025 2209 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A016755 | 1 27 125 343 729 1331 2197 3375 4913 6859 9261 12167 15625 19683 24389 29791 35937 42875 50653 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A000351 | 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A000420 | 1 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A085527 | 1 3 25 343 6561 161051 4826809 170859375 6975757441 322687697779 16679880978201 952809757913927 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A013609 | 1 1 2 1 4 4 1 6 12 8 1 8 24 32 16 1 10 40 80 80 32 1 12 60 160 240 192 64 1 14 84 280 560 672 448 |
| Inv | Accsee docs | missing | 1 -2 -1 4 0 1 -8 4 -2 -1 16 -16 8 0 1 -32 48 -32 8 -2 -1 64 -128 112 -48 12 0 1 -128 320 -352 208 |
| Inv | AccRevsee docs | A119258 | 1 1 -1 1 -3 1 1 -5 7 -1 1 -7 17 -15 1 1 -9 31 -49 31 -1 1 -11 49 -111 129 -63 1 1 -13 71 -209 351 |
| Inv | AntiDiagsee docs | A207538 | 1 -2 4 1 -8 -4 16 12 1 -32 -32 -6 64 80 24 1 -128 -192 -80 -8 256 448 240 40 1 -512 -1024 -672 -160 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -2 2 4 -8 3 -8 24 -18 4 16 -64 72 -32 5 -32 160 -240 160 -50 6 64 -384 720 -640 300 -72 7 -128 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A007051 | 1 -2 5 -14 41 -122 365 -1094 3281 -9842 29525 -88574 265721 -797162 2391485 -7174454 21523361 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A003462 | 0 1 -4 13 -40 121 -364 1093 -3280 9841 -29524 88573 -265720 797161 -2391484 7174453 -21523360 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A000129 | 1 -2 5 -12 29 -70 169 -408 985 -2378 5741 -13860 33461 -80782 195025 -470832 1136689 -2744210 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A005408 | 1 -3 5 -7 9 -11 13 -15 17 -19 21 -23 25 -27 29 -31 33 -35 37 -39 41 -43 45 -47 49 -51 53 -55 57 -59 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | 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 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 4 24 96 160 960 13440 35840 32256 322560 2365440 28385280 52715520 49201152 1476034560 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A171977 | 1 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 32 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 64 2 4 2 8 2 4 2 16 2 4 2 8 2 4 |
| Inv | RowMaxMax k=0..n | T(n, k) | | A109388 | 1 2 4 12 32 80 240 672 1792 5376 15360 42240 126720 366080 1025024 3075072 8945664 25346048 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -2 -4 12 24 -80 -160 560 1120 -4032 -8064 29568 59136 -219648 -439296 1647360 3294720 -12446720 |
| Inv | CentralET(2 n, n) | A059304 | 1 -4 24 -160 1120 -8064 59136 -439296 3294720 -24893440 189190144 -1444724736 11076222976 |
| Inv | CentralOT(2 n + 1, n) | A069723 | -2 12 -80 560 -4032 29568 -219648 1647360 -12446720 94595072 -722362368 5538111488 -42600857600 |
| Inv | ColLeftT(n, 0) | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| 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) | A098332 | 1 -1 -3 11 1 -81 141 363 -1791 479 13597 -29877 -54911 353807 -223443 -2539989 6806529 8302527 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A000027 | 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 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | 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 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A005563 | 0 1 0 -3 8 -15 24 -35 48 -63 80 -99 120 -143 168 -195 224 -255 288 -323 360 -399 440 -483 528 -575 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000351 | 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 |
| Inv | DiagRow1T(n + 1, n) | A005843 | -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50 -52 |
| Inv | DiagRow2T(n + 2, n) | A046092 | 4 12 24 40 60 84 112 144 180 220 264 312 364 420 480 544 612 684 760 840 924 1012 1104 1200 1300 |
| Inv | DiagRow3T(n + 3, n) | A130809 | -8 -32 -80 -160 -280 -448 -672 -960 -1320 -1760 -2288 -2912 -3640 -4480 -5440 -6528 -7752 -9120 |
| Inv | DiagCol1T(n + 1, 1) | A001787 | 1 -4 12 -32 80 -192 448 -1024 2304 -5120 11264 -24576 53248 -114688 245760 -524288 1114112 -2359296 |
| Inv | DiagCol2T(n + 2, 2) | A001788 | 1 -6 24 -80 240 -672 1792 -4608 11520 -28160 67584 -159744 372736 -860160 1966080 -4456448 10027008 |
| Inv | DiagCol3T(n + 3, 3) | A001789 | 1 -8 40 -160 560 -1792 5376 -15360 42240 -112640 292864 -745472 1863680 -4587520 11141120 -26738688 |
| Inv | Polysee docs | missing | 1 -2 1 4 -1 1 -8 1 0 1 16 -1 0 1 1 -32 1 0 1 2 1 64 -1 0 1 4 3 1 -128 1 0 1 8 9 4 1 256 -1 0 1 16 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -2 -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 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 4 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | -8 -1 0 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | 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 | PolyDiag∑ k=0..n T(n, k) n^k | A008788 | 1 -1 0 1 16 243 4096 78125 1679616 40353607 1073741824 31381059609 1000000000000 34522712143931 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A038207 | 1 2 1 4 4 1 8 12 6 1 16 32 24 8 1 32 80 80 40 10 1 64 192 240 160 60 12 1 128 448 672 560 280 84 14 |
| Inv:Rev | Accsee docs | A119258 | 1 1 -1 1 -3 1 1 -5 7 -1 1 -7 17 -15 1 1 -9 31 -49 31 -1 1 -11 49 -111 129 -63 1 1 -13 71 -209 351 |
| Inv:Rev | AccRevsee docs | missing | 1 -2 -1 4 0 1 -8 4 -2 -1 16 -16 8 0 1 -32 48 -32 8 -2 -1 64 -128 112 -48 12 0 1 -128 320 -352 208 |
| Inv:Rev | AntiDiagsee docs | A128099 | 1 1 1 -2 1 -4 1 -6 4 1 -8 12 1 -10 24 -8 1 -12 40 -32 1 -14 60 -80 16 1 -16 84 -160 80 1 -18 112 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -4 1 -8 12 1 -12 36 -32 1 -16 72 -128 80 1 -20 120 -320 400 -192 1 -24 180 -640 1200 -1152 448 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A046717 | 1 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453 21523361 64570081 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A152011 | 0 -2 -4 -14 -40 -122 -364 -1094 -3280 -9842 -29524 -88574 -265720 -797162 -2391484 -7174454 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A077020 | 1 1 -1 -3 -1 5 7 -3 -17 -11 23 45 -1 -91 -89 93 271 85 -457 -627 287 1541 967 -2115 -4049 181 8279 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | 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 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A005408 | 1 -3 5 -7 9 -11 13 -15 17 -19 21 -23 25 -27 29 -31 33 -35 37 -39 41 -43 45 -47 49 -51 53 -55 57 -59 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 4 24 96 160 960 13440 35840 32256 322560 2365440 28385280 52715520 49201152 1476034560 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A171977 | 1 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 32 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 64 2 4 2 8 2 4 2 16 2 4 2 8 2 4 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | A109388 | 1 2 4 12 32 80 240 672 1792 5376 15360 42240 126720 366080 1025024 3075072 8945664 25346048 |
| Inv:Rev | ColMiddleT(n, n // 2) | A098660 | 1 1 -4 -6 24 40 -160 -280 1120 2016 -8064 -14784 59136 109824 -439296 -823680 3294720 6223360 |
| Inv:Rev | CentralET(2 n, n) | A059304 | 1 -4 24 -160 1120 -8064 59136 -439296 3294720 -24893440 189190144 -1444724736 11076222976 |
| Inv:Rev | CentralOT(2 n + 1, n) | A069720 | 1 -6 40 -280 2016 -14784 109824 -823680 6223360 -47297536 361181184 -2769055744 21300428800 |
| 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) | A000079 | 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A098332 | 1 -1 -3 11 1 -81 141 363 -1791 479 13597 -29877 -54911 353807 -223443 -2539989 6806529 8302527 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A001850 | 1 -3 13 -63 321 -1683 8989 -48639 265729 -1462563 8097453 -45046719 251595969 -1409933619 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A005843 | 0 -2 4 -6 8 -10 12 -14 16 -18 20 -22 24 -26 28 -30 32 -34 36 -38 40 -42 44 -46 48 -50 52 -54 56 -58 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A005408 | 1 -3 5 -7 9 -11 13 -15 17 -19 21 -23 25 -27 29 -31 33 -35 37 -39 41 -43 45 -47 49 -51 53 -55 57 -59 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A002939 | 0 -2 12 -30 56 -90 132 -182 240 -306 380 -462 552 -650 756 -870 992 -1122 1260 -1406 1560 -1722 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000302 | 1 -4 16 -64 256 -1024 4096 -16384 65536 -262144 1048576 -4194304 16777216 -67108864 268435456 |
| Inv:Rev | DiagRow1T(n + 1, n) | A001787 | 1 -4 12 -32 80 -192 448 -1024 2304 -5120 11264 -24576 53248 -114688 245760 -524288 1114112 -2359296 |
| Inv:Rev | DiagRow2T(n + 2, n) | A001788 | 1 -6 24 -80 240 -672 1792 -4608 11520 -28160 67584 -159744 372736 -860160 1966080 -4456448 10027008 |
| Inv:Rev | DiagRow3T(n + 3, n) | A001789 | 1 -8 40 -160 560 -1792 5376 -15360 42240 -112640 292864 -745472 1863680 -4587520 11141120 -26738688 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A005843 | -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50 -52 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A046092 | 4 12 24 40 60 84 112 144 180 220 264 312 364 420 480 544 612 684 760 840 924 1012 1104 1200 1300 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A130809 | -8 -32 -80 -160 -280 -448 -672 -960 -1320 -1760 -2288 -2912 -3640 -4480 -5440 -6528 -7752 -9120 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 -1 1 1 1 -3 1 1 -1 9 -5 1 1 1 -27 25 -7 1 1 -1 81 -125 49 -9 1 1 1 -243 625 -343 81 -11 1 1 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A005408 | 1 -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A016754 | 1 1 9 25 49 81 121 169 225 289 361 441 529 625 729 841 961 1089 1225 1369 1521 1681 1849 2025 2209 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A016755 | 1 -1 -27 -125 -343 -729 -1331 -2197 -3375 -4913 -6859 -9261 -12167 -15625 -19683 -24389 -29791 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A000351 | 1 -5 25 -125 625 -3125 15625 -78125 390625 -1953125 9765625 -48828125 244140625 -1220703125 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A085528 | 1 -1 9 -125 2401 -59049 1771561 -62748517 2562890625 -118587876497 6131066257801 -350277500542221 |
| << | 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.