OEIS Similars: A123125, A173018, A008292
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A173018 | 1 0 1 0 1 1 0 1 4 1 0 1 11 11 1 0 1 26 66 26 1 0 1 57 302 302 57 1 0 1 120 1191 2416 1191 120 1 0 1 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A173018 | 1 1 0 1 1 0 1 4 1 0 1 11 11 1 0 1 26 66 26 1 0 1 57 302 302 57 1 0 1 120 1191 2416 1191 120 1 0 1 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 3 -4 1 0 -23 33 -11 1 0 425 -620 220 -26 1 0 -18129 26525 -9520 1180 -57 1 0 1721419 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -4 3 0 1 -11 33 -23 0 1 -26 220 -620 425 0 1 -57 1180 -9520 26525 -18129 0 1 -120 |
| Std | Accsee docs | missing | 1 0 1 0 1 2 0 1 5 6 0 1 12 23 24 0 1 27 93 119 120 0 1 58 360 662 719 720 0 1 121 1312 3728 4919 |
| Std | AccRevsee docs | missing | 1 1 1 1 2 2 1 5 6 6 1 12 23 24 24 1 27 93 119 120 120 1 58 360 662 719 720 720 1 121 1312 3728 4919 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 1 0 1 1 0 1 4 0 1 11 1 0 1 26 11 0 1 57 66 1 0 1 120 302 26 0 1 247 1191 302 1 0 1 502 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 2 3 0 2 12 4 0 2 33 44 5 0 2 78 264 130 6 0 2 171 1208 1510 342 7 0 2 360 4764 12080 7146 |
| Std | RowSum∑ k=0..n T(n, k) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A262745 | 1 0 1 4 12 52 360 2656 20160 177472 1814400 20135296 239500800 3102326272 43589145600 654789062656 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A128103 | 0 1 1 2 12 68 360 2384 20160 185408 1814400 19781504 239500800 3124694528 43589145600 652885305344 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A009006 | 1 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A000800 | 1 0 1 1 2 5 13 38 125 449 1742 7269 32433 153850 772397 4088773 22746858 132601933 807880821 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001710 | 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A038720 | 1 2 5 18 84 480 3240 25200 221760 2177280 23587200 279417600 3592512000 49816166400 741015475200 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A180057 | 1 1 1 4 11 858 17214 14387280 16561934649 12632627296395920 1806607850839536160 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 4 11 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | A006551 | 1 1 1 4 11 66 302 2416 15619 156190 1310354 15724248 162512286 2275172004 27971176092 447538817472 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 1 1 11 26 302 1191 15619 88234 1310354 9738114 162512286 1505621508 27971176092 311387598411 |
| Std | CentralET(2 n, n) | A180056 | 1 1 11 302 15619 1310354 162512286 27971176092 6382798925475 1865385657780650 679562217794156938 |
| Std | CentralOT(2 n + 1, n) | missing | 0 1 26 1191 88234 9738114 1505621508 311387598411 83137223185370 27862280567093358 |
| Std | ColLeftT(n, 0) | 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 |
| 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) | A011818 | 1 1 3 16 115 1056 11774 154624 2337507 39984640 763546234 16101629952 371644257582 9319104528384 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344052 | 1 1 -1 -8 19 276 -1002 -21216 103395 2881180 -17620142 -609297072 4483215086 185182296040 |
| Std | TransNat0∑ k=0..n T(n, k) k | A001710 | 0 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A038720 | 1 2 5 18 84 480 3240 25200 221760 2177280 23587200 279417600 3592512000 49816166400 741015475200 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 5 26 160 1140 9240 84000 846720 9374400 113097600 1476921600 20756736000 312388876800 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000670 | 1 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A212846 | 1 1 -1 -3 15 21 -441 477 19935 -101979 -1150281 14838957 60479055 -2328851979 3529587879 |
| Std | DiagRow1T(n + 1, n) | A000295 | 0 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752 65519 131054 262125 524268 1048555 |
| Std | DiagRow2T(n + 2, n) | A000460 | 0 1 11 66 302 1191 4293 14608 47840 152637 478271 1479726 4537314 13824739 41932745 126781020 |
| Std | DiagRow3T(n + 3, n) | A000498 | 0 1 26 302 2416 15619 88234 455192 2203488 10187685 45533450 198410786 848090912 3572085255 |
| Std | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A000295 | 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752 65519 131054 262125 524268 1048555 2097130 |
| Std | DiagCol3T(n + 3, 3) | A000460 | 1 11 66 302 1191 4293 14608 47840 152637 478271 1479726 4537314 13824739 41932745 126781020 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 6 6 3 1 0 24 26 12 4 1 0 120 150 66 20 5 1 0 720 1082 480 132 30 6 1 0 5040 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^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 31 32 33 34 35 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 6 26 66 132 230 366 546 776 1062 1410 1826 2316 2886 3542 4290 5136 6086 7146 8322 9620 11046 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A123227 | 1 3 12 66 480 4368 47712 608016 8855040 145083648 2641216512 52891055616 1155444326400 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A122020 | 1 1 6 66 1140 28280 948570 41173776 2238150600 148570107264 11804909261310 1104566746764800 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A173018 | 1 0 -1 0 -1 1 0 -1 4 -1 0 -1 11 -11 1 0 -1 26 -66 26 -1 0 -1 57 -302 302 -57 1 0 -1 120 -1191 2416 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A173018 | 1 -1 0 1 -1 0 -1 4 -1 0 1 -11 11 -1 0 -1 26 -66 26 -1 0 1 -57 302 -302 57 -1 0 -1 120 -1191 2416 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 -3 -4 1 0 -43 -55 11 1 0 895 1140 -220 -26 1 0 63039 80325 -15560 -1784 57 1 0 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -4 -3 0 1 11 -55 -43 0 1 -26 -220 1140 895 0 1 57 -1784 -15560 80325 63039 0 1 -120 |
| Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 -1 3 2 0 -1 10 -1 0 0 -1 25 -41 -15 -16 0 -1 56 -246 56 -1 0 0 -1 119 -1072 1344 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 3 2 2 1 -10 1 0 0 -1 25 -41 -15 -16 -16 1 -56 246 -56 1 0 0 -1 119 -1072 1344 153 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -1 0 -1 1 0 -1 4 0 -1 11 -1 0 -1 26 -11 0 -1 57 -66 1 0 -1 120 -302 26 0 -1 247 -1191 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -2 3 0 -2 12 -4 0 -2 33 -44 5 0 -2 78 -264 130 -6 0 -2 171 -1208 1510 -342 7 0 -2 360 |
| Alt | RowSum∑ k=0..n T(n, k) | A009006 | 1 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A262745 | 1 0 1 4 12 52 360 2656 20160 177472 1814400 20135296 239500800 3102326272 43589145600 654789062656 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A128103 | 0 -1 -1 -2 -12 -68 -360 -2384 -20160 -185408 -1814400 -19781504 -239500800 -3124694528 -43589145600 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -1 0 3 9 14 -9 -157 -644 -1433 833 26930 154739 511027 281960 -10020029 -85807959 -420141258 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 4 8 -48 -136 1088 3968 -39680 -176896 2122752 11184128 -156577792 -951878656 15230058496 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 1 6 -8 -64 136 1360 -3968 -47616 176896 2476544 -11184128 -178946048 951878656 17133815808 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A180057 | 1 1 1 4 11 858 17214 14387280 16561934649 12632627296395920 1806607850839536160 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 4 11 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A006551 | 1 1 1 4 11 66 302 2416 15619 156190 1310354 15724248 162512286 2275172004 27971176092 447538817472 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -1 -1 11 26 -302 -1191 15619 88234 -1310354 -9738114 162512286 1505621508 -27971176092 |
| Alt | CentralET(2 n, n) | A180056 | 1 -1 11 -302 15619 -1310354 162512286 -27971176092 6382798925475 -1865385657780650 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -1 26 -1191 88234 -9738114 1505621508 -311387598411 83137223185370 -27862280567093358 |
| Alt | ColLeftT(n, 0) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A344052 | 1 -1 -1 8 19 -276 -1002 21216 103395 -2881180 -17620142 609297072 4483215086 -185182296040 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A011818 | 1 -1 3 -16 115 -1056 11774 -154624 2337507 -39984640 763546234 -16101629952 371644257582 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 1 4 -8 -48 136 1088 -3968 -39680 176896 2122752 -11184128 -156577792 951878656 15230058496 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 1 6 -8 -64 136 1360 -3968 -47616 176896 2476544 -11184128 -178946048 951878656 17133815808 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 3 6 -40 -100 952 2912 -35712 -129792 1945856 8205824 -145393664 -698394112 14278179840 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A212846 | 1 -1 -1 3 15 -21 -441 -477 19935 101979 -1150281 -14838957 60479055 2328851979 3529587879 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000670 | 1 -1 3 -13 75 -541 4683 -47293 545835 -7087261 102247563 -1622632573 28091567595 -526858348381 |
| Alt | DiagRow1T(n + 1, n) | A000295 | 0 -1 4 -11 26 -57 120 -247 502 -1013 2036 -4083 8178 -16369 32752 -65519 131054 -262125 524268 |
| Alt | DiagRow2T(n + 2, n) | A000460 | 0 -1 11 -66 302 -1191 4293 -14608 47840 -152637 478271 -1479726 4537314 -13824739 41932745 |
| Alt | DiagRow3T(n + 3, n) | A000498 | 0 -1 26 -302 2416 -15619 88234 -455192 2203488 -10187685 45533450 -198410786 848090912 -3572085255 |
| Alt | DiagCol1T(n + 1, 1) | 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 |
| Alt | DiagCol2T(n + 2, 2) | A000295 | 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752 65519 131054 262125 524268 1048555 2097130 |
| Alt | DiagCol3T(n + 3, 3) | A000460 | -1 -11 -66 -302 -1191 -4293 -14608 -47840 -152637 -478271 -1479726 -4537314 -13824739 -41932745 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 0 -2 1 0 2 2 -3 1 0 0 6 6 -4 1 0 -16 -30 6 12 -5 1 0 0 -42 -120 -4 20 -6 1 0 272 882 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^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 | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 2 6 6 -4 -30 -78 -154 -264 -414 -610 -858 -1164 -1534 -1974 -2490 -3088 -3774 -4554 -5434 -6420 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A179929 | 1 -2 2 6 -30 -42 882 -954 -39870 203958 2300562 -29677914 -120958110 4657703958 -7059175758 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 6 6 -120 312 3696 -39504 -48000 4451712 -29086464 -453483264 9863992320 440282112 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 2 6 -276 5520 -68370 -1324624 174154680 -10410981120 412902781290 1502342214912 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A173018 | 1 1 0 1 1 0 1 4 1 0 1 11 11 1 0 1 26 66 26 1 0 1 57 302 302 57 1 0 1 120 1191 2416 1191 120 1 0 1 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 3 -4 1 0 -23 33 -11 1 0 425 -620 220 -26 1 0 -18129 26525 -9520 1180 -57 1 0 1721419 |
| Rev | Accsee docs | missing | 1 1 1 1 2 2 1 5 6 6 1 12 23 24 24 1 27 93 119 120 120 1 58 360 662 719 720 720 1 121 1312 3728 4919 |
| Rev | AccRevsee docs | missing | 1 0 1 0 1 2 0 1 5 6 0 1 12 23 24 0 1 27 93 119 120 0 1 58 360 662 719 720 0 1 121 1312 3728 4919 |
| Rev | AntiDiagsee docs | A344393 | 1 1 1 0 1 1 1 4 0 1 11 1 1 26 11 0 1 57 66 1 1 120 302 26 0 1 247 1191 302 1 1 502 4293 2416 57 0 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 8 3 0 1 22 33 4 0 1 52 198 104 5 0 1 114 906 1208 285 6 0 1 240 3573 9664 5955 720 7 |
| Rev | RowSum∑ k=0..n T(n, k) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A128103 | 1 1 1 2 12 68 360 2384 20160 185408 1814400 19781504 239500800 3124694528 43589145600 652885305344 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A262745 | 0 0 1 4 12 52 360 2656 20160 177472 1814400 20135296 239500800 3102326272 43589145600 654789062656 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A009006 | 1 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A000800 | 1 1 1 2 5 13 38 125 449 1742 7269 32433 153850 772397 4088773 22746858 132601933 807880821 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A038720 | 1 2 5 18 84 480 3240 25200 221760 2177280 23587200 279417600 3592512000 49816166400 741015475200 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001710 | 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A180057 | 1 1 1 4 11 858 17214 14387280 16561934649 12632627296395920 1806607850839536160 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 4 11 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A006551 | 1 1 1 4 11 66 302 2416 15619 156190 1310354 15724248 162512286 2275172004 27971176092 447538817472 |
| Rev | ColMiddleT(n, n // 2) | A006551 | 1 1 1 4 11 66 302 2416 15619 156190 1310354 15724248 162512286 2275172004 27971176092 447538817472 |
| Rev | CentralET(2 n, n) | A180056 | 1 1 11 302 15619 1310354 162512286 27971176092 6382798925475 1865385657780650 679562217794156938 |
| Rev | CentralOT(2 n + 1, n) | A025585 | 1 4 66 2416 156190 15724248 2275172004 447538817472 114890380658550 37307713155613000 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A011818 | 1 1 3 16 115 1056 11774 154624 2337507 39984640 763546234 16101629952 371644257582 9319104528384 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344052 | 1 -1 -1 8 19 -276 -1002 21216 103395 -2881180 -17620142 609297072 4483215086 -185182296040 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A001286 | 0 0 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A001710 | 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A344054 | 0 0 1 8 64 540 4920 48720 524160 6108480 76809600 1037836800 15008716800 231437606400 3792255667200 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000629 | 1 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A179929 | 1 -2 2 6 -30 -42 882 -954 -39870 203958 2300562 -29677914 -120958110 4657703958 -7059175758 |
| Rev | DiagRow1T(n + 1, 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 |
| Rev | DiagRow2T(n + 2, n) | A000295 | 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752 65519 131054 262125 524268 1048555 2097130 |
| Rev | DiagRow3T(n + 3, n) | A000460 | 1 11 66 302 1191 4293 14608 47840 152637 478271 1479726 4537314 13824739 41932745 126781020 |
| Rev | DiagCol1T(n + 1, 1) | A000295 | 0 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752 65519 131054 262125 524268 1048555 |
| Rev | DiagCol2T(n + 2, 2) | A000460 | 0 1 11 66 302 1191 4293 14608 47840 152637 478271 1479726 4537314 13824739 41932745 126781020 |
| Rev | DiagCol3T(n + 3, 3) | A000498 | 0 1 26 302 2416 15619 88234 455192 2203488 10187685 45533450 198410786 848090912 3572085255 |
| Rev | Polysee docs | A332700 | 1 1 1 1 1 1 1 2 1 1 1 6 3 1 1 1 24 13 4 1 1 1 120 75 22 5 1 1 1 720 541 160 33 6 1 1 1 5040 4683 |
| Rev | PolyRow1∑ k=0..1 T(1, k) 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 |
| Rev | PolyRow2∑ k=0..2 T(2, 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 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A028872 | 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 726 781 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A000670 | 1 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A122704 | 1 1 4 22 160 1456 15904 202672 2951680 48361216 880405504 17630351872 385148108800 9114999832576 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A122778 | 1 1 3 22 285 5656 158095 5881968 279768825 16507789696 1180490926131 100415158796800 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 3 -4 1 0 -23 33 -11 1 0 425 -620 220 -26 1 0 -18129 26525 -9520 1180 -57 1 0 1721419 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -4 3 0 1 -11 33 -23 0 1 -26 220 -620 425 0 1 -57 1180 -9520 26525 -18129 0 1 -120 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A173018 | 1 1 0 1 1 0 1 4 1 0 1 11 11 1 0 1 26 66 26 1 0 1 57 302 302 57 1 0 1 120 1191 2416 1191 120 1 0 1 |
| Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 3 -1 0 0 -23 10 -1 0 0 425 -195 25 -1 0 0 -18129 8396 -1124 56 -1 0 0 1721419 |
| Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 -3 0 0 1 -10 23 0 0 1 -25 195 -425 0 0 1 -56 1124 -8396 18129 0 0 1 -119 5530 -107520 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 3 1 0 -23 -4 0 425 33 1 0 -18129 -620 -11 0 1721419 26525 220 1 0 -353654167 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 6 -12 4 0 -46 99 -44 5 0 850 -1860 880 -130 6 0 -36258 79575 -38080 5900 -342 7 0 |
| Inv | RowSum∑ k=0..n T(n, k) | A019590 | 1 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 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 -4 34 -646 27706 -2632834 540943894 -235440050206 213784986478426 -400496123507752834 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -1 4 -34 646 -27706 2632834 -540943894 235440050206 -213784986478426 400496123507752834 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -1 2 -8 68 -1292 55412 -5265668 1081887788 -470880100412 427569972956852 -800992247015505668 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 8 68 1292 55412 5265668 1081887788 470880100412 427569972956852 800992247015505668 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -1 4 -27 459 -18760 1748165 -356183377 154441679984 -139991150863463 262035970469968235 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 2 -14 254 -10802 1025282 -210628574 91672862654 -83241011160482 155940328618482242 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 1 -2 14 -254 10802 -1025282 210628574 -91672862654 83241011160482 -155940328618482242 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 12 759 7536100 1026364915892400 261891765713181433200 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 4 33 620 26525 2519664 517670461 225309742552 204586385695065 383263833094891100 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -1 3 33 -620 -9520 905765 23248085 -10119247684 -461102826618 863812603482906 72133429144708470 |
| Inv | CentralET(2 n, n) | missing | 1 -1 33 -9520 23248085 -461102826618 72133429144708470 -87969630451614365600718 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 3 -620 905765 -10119247684 863812603482906 -562517197939195769556 2804781888582977542701824505 |
| Inv | ColLeftT(n, 0) | 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 | 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 1 -1 -2 63 -2004 116060 -13000196 2805402383 -1133051255552 797251531657020 -752227446454305678 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 3 22 335 10656 715092 100740872 29440294767 17641158624220 21478935357883652 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 1 -2 14 -254 10802 -1025282 210628574 -91672862654 83241011160482 -155940328618482242 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 1 -2 14 -254 10802 -1025282 210628574 -91672862654 83241011160482 -155940328618482242 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 -4 26 -466 19782 -1877198 385632634 -167840371410 152402794095350 -285505201096326190 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 5 -73 2669 -227281 43151765 -17730027673 15433466711549 -28027868889140641 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 3 21 339 12693 1085523 206219541 84735988179 73760569610133 133952554990485843 |
| Inv | DiagRow1T(n + 1, n) | A000295 | 0 -1 -4 -11 -26 -57 -120 -247 -502 -1013 -2036 -4083 -8178 -16369 -32752 -65519 -131054 -262125 |
| Inv | DiagRow2T(n + 2, n) | missing | 0 3 33 220 1180 5649 25347 109386 460686 1909831 7834717 31911048 129328368 522292749 2103945543 |
| Inv | DiagRow3T(n + 3, n) | missing | 0 -23 -620 -9520 -113050 -1166221 -11059468 -99446730 -863536410 -7323539135 -61105126940 |
| Inv | DiagCol1T(n + 1, 1) | A055326 | 1 -1 3 -23 425 -18129 1721419 -353654167 153923102577 -139765654884545 261831303051976691 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -4 33 -620 26525 -2519664 517670461 -225309742552 204586385695065 -383263833094891100 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -11 220 -9520 905765 -186123259 81009042744 -73558129319520 137800821538668585 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 0 2 3 1 0 0 -2 6 4 1 0 0 14 0 12 5 1 0 0 -254 12 12 20 6 1 0 0 10802 -228 -12 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^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 31 32 33 34 35 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 0 -2 0 12 40 90 168 280 432 630 880 1188 1560 2002 2520 3120 3808 4590 5472 6460 7560 8778 10120 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 2 -2 14 -254 10802 -1025282 210628574 -91672862654 83241011160482 -155940328618482242 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 6 0 12 -228 9756 -926700 190391172 -82865376468 75243648657756 -140958397763559660 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 2 0 -12 1000 -77490 9479148 -1840661368 407756323728 372685323181050 -2870310547784125820 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -4 3 0 1 -11 33 -23 0 1 -26 220 -620 425 0 1 -57 1180 -9520 26525 -18129 0 1 -120 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 3 -4 1 0 -23 33 -11 1 0 425 -620 220 -26 1 0 -18129 26525 -9520 1180 -57 1 0 1721419 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A173018 | 1 0 1 0 1 1 0 1 4 1 0 1 11 11 1 0 1 26 66 26 1 0 1 57 302 302 57 1 0 1 120 1191 2416 1191 120 1 0 1 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 -3 0 0 1 -10 23 0 0 1 -25 195 -425 0 0 1 -56 1124 -8396 18129 0 0 1 -119 5530 -107520 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 3 -1 0 0 -23 10 -1 0 0 425 -195 25 -1 0 0 -18129 8396 -1124 56 -1 0 0 1721419 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -4 0 1 -11 3 1 -26 33 0 1 -57 220 -23 1 -120 1180 -620 0 1 -247 5649 -9520 425 1 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -8 9 0 1 -22 99 -92 0 1 -52 660 -2480 2125 0 1 -114 3540 -38080 132625 -108774 0 1 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A019590 | 1 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 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 4 34 646 27706 2632834 540943894 235440050206 213784986478426 400496123507752834 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -1 -4 -34 -646 -27706 -2632834 -540943894 -235440050206 -213784986478426 -400496123507752834 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 1 2 8 68 1292 55412 5265668 1081887788 470880100412 427569972956852 800992247015505668 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 8 68 1292 55412 5265668 1081887788 470880100412 427569972956852 800992247015505668 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 -3 -7 8 141 441 -3692 -61679 -170211 10127604 225852677 -413333803 -201427367676 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 1 -2 14 -254 10802 -1025282 210628574 -91672862654 83241011160482 -155940328618482242 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 2 -14 254 -10802 1025282 -210628574 91672862654 -83241011160482 155940328618482242 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 12 759 7536100 1026364915892400 261891765713181433200 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 4 33 620 26525 2519664 517670461 225309742552 204586385695065 383263833094891100 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -1 -4 33 220 -9520 -113050 23248085 507795498 -461102826618 -18816103842228 72133429144708470 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -1 33 -9520 23248085 -461102826618 72133429144708470 -87969630451614365600718 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -4 220 -113050 507795498 -18816103842228 5569899127407415086 -13000182161456131108373478 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -1 -2 63 -2004 116060 -13000196 2805402383 -1133051255552 797251531657020 -752227446454305678 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -22 335 -10656 715092 -100740872 29440294767 -17641158624220 21478935357883652 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -1 2 -14 254 -10802 1025282 -210628574 91672862654 -83241011160482 155940328618482242 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 2 -14 254 -10802 1025282 -210628574 91672862654 -83241011160482 155940328618482242 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 8 -86 2074 -109842 12476750 -2984424550 1482271156362 -1512417429114290 3145182028510283134 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 2 -2 14 -254 10802 -1025282 210628574 -91672862654 83241011160482 -155940328618482242 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 6 -30 282 -5538 239286 -22764990 4677918762 -2036036872578 1848769740114726 |
| Inv:Rev | DiagRow1T(n + 1, n) | A055326 | 1 -1 3 -23 425 -18129 1721419 -353654167 153923102577 -139765654884545 261831303051976691 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -4 33 -620 26525 -2519664 517670461 -225309742552 204586385695065 -383263833094891100 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -11 220 -9520 905765 -186123259 81009042744 -73558129319520 137800821538668585 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000295 | 0 -1 -4 -11 -26 -57 -120 -247 -502 -1013 -2036 -4083 -8178 -16369 -32752 -65519 -131054 -262125 |
| Inv:Rev | DiagCol2T(n + 2, 2) | missing | 0 3 33 220 1180 5649 25347 109386 460686 1909831 7834717 31911048 129328368 522292749 2103945543 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | 0 -23 -620 -9520 -113050 -1166221 -11059468 -99446730 -863536410 -7323539135 -61105126940 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 0 -1 1 1 1 0 5 -2 1 1 1 0 -73 16 -3 1 1 1 0 2669 -356 33 -4 1 1 1 0 -227281 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) 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 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, 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 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A045944 | 1 0 5 16 33 56 85 120 161 208 261 320 385 456 533 616 705 800 901 1008 1121 1240 1365 1496 1633 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 5 -73 2669 -227281 43151765 -17730027673 15433466711549 -28027868889140641 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -2 16 -356 19588 -2503412 713001196 -439436014796 573774517832308 -1563000516883257332 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -1 16 -987 193496 -108608885 162311472660 -611966596583671 5590692656883490672 |
| << | 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.