OEIS Similars: A132393, A008275, A008276, A048994, A054654, A094638, A130534
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A132393 | 1 0 1 0 1 1 0 2 3 1 0 6 11 6 1 0 24 50 35 10 1 0 120 274 225 85 15 1 0 720 1764 1624 735 175 21 1 0 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A054654 | 1 1 0 1 1 0 1 3 2 0 1 6 11 6 0 1 10 35 50 24 0 1 15 85 225 274 120 0 1 21 175 735 1624 1764 720 0 1 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A048993 | 1 0 1 0 -1 1 0 1 -3 1 0 -1 7 -6 1 0 1 -15 25 -10 1 0 -1 31 -90 65 -15 1 0 1 -63 301 -350 140 -21 1 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A106800 | 1 1 0 1 -1 0 1 -3 1 0 1 -6 7 -1 0 1 -10 25 -15 1 0 1 -15 65 -90 31 -1 0 1 -21 140 -350 301 -63 1 0 |
| Std | Accsee docs | A349782 | 1 0 1 0 1 2 0 2 5 6 0 6 17 23 24 0 24 74 109 119 120 0 120 394 619 704 719 720 0 720 2484 4108 4843 |
| Std | AccRevsee docs | A096747 | 1 1 1 1 2 2 1 4 6 6 1 7 18 24 24 1 11 46 96 120 120 1 16 101 326 600 720 720 1 22 197 932 2556 4320 |
| Std | AntiDiagsee docs | A331327 | 1 0 0 1 0 1 0 2 1 0 6 3 0 24 11 1 0 120 50 6 0 720 274 35 1 0 5040 1764 225 10 0 40320 13068 1624 |
| Std | Diffx1T(n, k) (k+1) | A360174 | 1 0 2 0 2 3 0 4 9 4 0 12 33 24 5 0 48 150 140 50 6 0 240 822 900 425 90 7 0 1440 5292 6496 3675 |
| 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) | A001710 | 1 0 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A001710 | 0 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| 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) | A343579 | 1 0 1 1 3 9 36 176 1030 7039 55098 486346 4780445 51787405 613045468 7873065045 109021348618 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A121586 | 1 1 3 13 70 446 3276 27252 253296 2602224 29288160 358457760 4740577920 67375532160 1024208720640 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000774 | 1 2 5 17 74 394 2484 18108 149904 1389456 14257440 160460640 1965444480 26029779840 370643938560 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A063039 | 1 1 1 6 66 4200 4192200 5115600 19083776176080 10086416728304192640 126556188275836361347200 |
| Std | 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | A065048 | 1 1 1 3 11 50 274 1764 13132 118124 1172700 12753576 150917976 1931559552 26596717056 392156797824 |
| Std | ColMiddleT(n, n // 2) | A154415 | 1 0 1 2 11 50 225 1624 6769 67284 269325 3416930 13339535 206070150 790943153 14409322928 |
| Std | CentralET(2 n, n) | A187646 | 1 1 11 225 6769 269325 13339535 790943153 54631129553 4308105301929 381922055502195 |
| Std | CentralOT(2 n + 1, n) | A367777 | 0 2 50 1624 67284 3416930 206070150 14409322928 1146901283528 102417740732658 10142299865511450 |
| 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) | A211210 | 1 1 3 16 115 1021 10696 128472 1734447 25937683 424852351 7554471156 144767131444 2971727661124 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A317274 | 1 1 -1 -2 19 -79 76 2640 -36945 329371 -1861949 -4438774 355714228 -7292531180 109844527612 |
| Std | TransNat0∑ k=0..n T(n, k) k | A000254 | 0 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A000774 | 1 2 5 17 74 394 2484 18108 149904 1389456 14257440 160460640 1965444480 26029779840 370643938560 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A151881 | 0 1 5 23 120 724 5012 39332 345832 3371976 36135792 422379792 5349561984 72996193152 1067779243008 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001147 | 1 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
| Std | DiagRow1T(n + 1, n) | A000217 | 0 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 |
| Std | DiagRow2T(n + 2, n) | A000914 | 0 2 11 35 85 175 322 546 870 1320 1925 2717 3731 5005 6580 8500 10812 13566 16815 20615 25025 30107 |
| Std | DiagRow3T(n + 3, n) | A001303 | 0 6 50 225 735 1960 4536 9450 18150 32670 55770 91091 143325 218400 323680 468180 662796 920550 |
| Std | DiagCol1T(n + 1, 1) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | DiagCol2T(n + 2, 2) | A000254 | 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Std | DiagCol3T(n + 3, 3) | A000399 | 1 6 35 225 1624 13132 118124 1172700 12753576 150917976 1931559552 26596717056 392156797824 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 6 6 3 1 0 24 24 12 4 1 0 120 120 60 20 5 1 0 720 720 360 120 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 | A007531 | 0 6 24 60 120 210 336 504 720 990 1320 1716 2184 2730 3360 4080 4896 5814 6840 7980 9240 10626 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A001710 | 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A000407 | 1 1 6 60 840 15120 332640 8648640 259459200 8821612800 335221286400 14079294028800 647647525324800 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 -1 -3 1 0 -11 -29 6 1 0 49 135 -25 -10 1 0 1291 3541 -660 -235 15 1 0 -13119 -36057 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -3 -1 0 1 6 -29 -11 0 1 -10 -25 135 49 0 1 15 -235 -660 3541 1291 0 1 -21 -140 2450 |
| Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 -2 1 0 0 -6 5 -1 0 0 -24 26 -9 1 0 0 -120 154 -71 14 -1 0 0 -720 1044 -580 155 -20 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 2 0 0 1 -5 6 0 0 -1 9 -26 24 0 0 1 -14 71 -154 120 0 0 -1 20 -155 580 -1044 720 0 |
| Alt | AntiDiagsee docs | A331327 | 1 0 0 -1 0 -1 0 -2 1 0 -6 3 0 -24 11 -1 0 -120 50 -6 0 -720 274 -35 1 0 -5040 1764 -225 10 0 -40320 |
| Alt | Diffx1T(n, k) (k+1) | A360174 | 1 0 -2 0 -2 3 0 -4 9 -4 0 -12 33 -24 5 0 -48 150 -140 50 -6 0 -240 822 -900 425 -90 7 0 -1440 5292 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A001710 | 1 0 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A001710 | 0 -1 -1 -3 -12 -60 -360 -2520 -20160 -181440 -1814400 -19958400 -239500800 -3113510400 -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) | A353253 | 1 0 -1 -1 -1 -3 -14 -76 -480 -3491 -28792 -265708 -2713753 -30395515 -370509784 -4883351213 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000142 | 1 -1 -1 -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000142 | 1 -2 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A063039 | 1 1 1 6 66 4200 4192200 5115600 19083776176080 10086416728304192640 126556188275836361347200 |
| Alt | 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A065048 | 1 1 1 3 11 50 274 1764 13132 118124 1172700 12753576 150917976 1931559552 26596717056 392156797824 |
| Alt | ColMiddleT(n, n // 2) | A154415 | 1 0 -1 -2 11 50 -225 -1624 6769 67284 -269325 -3416930 13339535 206070150 -790943153 -14409322928 |
| Alt | CentralET(2 n, n) | A187646 | 1 -1 11 -225 6769 -269325 13339535 -790943153 54631129553 -4308105301929 381922055502195 |
| Alt | CentralOT(2 n + 1, n) | A367777 | 0 -2 50 -1624 67284 -3416930 206070150 -14409322928 1146901283528 -102417740732658 |
| 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) | A317274 | 1 -1 -1 2 19 79 76 -2640 -36945 -329371 -1861949 4438774 355714228 7292531180 109844527612 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A211210 | 1 -1 3 -16 115 -1021 10696 -128472 1734447 -25937683 424852351 -7554471156 144767131444 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000142 | 0 -1 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000142 | 1 -2 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A045406 | 0 -1 3 1 0 -4 -28 -188 -1368 -11016 -98208 -964512 -10370880 -121337280 -1535880960 -20924455680 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001147 | 1 -1 -1 -3 -15 -105 -945 -10395 -135135 -2027025 -34459425 -654729075 -13749310575 -316234143225 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001147 | 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
| Alt | DiagRow1T(n + 1, n) | A000217 | 0 -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 | DiagRow2T(n + 2, n) | A000914 | 0 -2 11 -35 85 -175 322 -546 870 -1320 1925 -2717 3731 -5005 6580 -8500 10812 -13566 16815 -20615 |
| Alt | DiagRow3T(n + 3, n) | A001303 | 0 -6 50 -225 735 -1960 4536 -9450 18150 -32670 55770 -91091 143325 -218400 323680 -468180 662796 |
| Alt | DiagCol1T(n + 1, 1) | A000142 | -1 -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 |
| Alt | DiagCol2T(n + 2, 2) | A000254 | 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Alt | DiagCol3T(n + 3, 3) | A000399 | -1 -6 -35 -225 -1624 -13132 -118124 -1172700 -12753576 -150917976 -1931559552 -26596717056 |
| Alt | Polysee docs | A122851 | 1 0 1 0 -1 1 0 0 -2 1 0 0 2 -3 1 0 0 0 6 -4 1 0 0 0 -6 12 -5 1 0 0 0 0 -24 20 -6 1 0 0 0 0 24 -60 |
| 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 | A007531 | 0 0 0 -6 -24 -60 -120 -210 -336 -504 -720 -990 -1320 -1716 -2184 -2730 -3360 -4080 -4896 -5814 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 2 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 | PolyCol3∑ k=0..n T(n, k) 3^k | A186685 | 1 -3 6 -6 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 | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A054654 | 1 1 0 1 1 0 1 3 2 0 1 6 11 6 0 1 10 35 50 24 0 1 15 85 225 274 120 0 1 21 175 735 1624 1764 720 0 1 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A048993 | 1 0 1 0 -1 1 0 1 -3 1 0 -1 7 -6 1 0 1 -15 25 -10 1 0 -1 31 -90 65 -15 1 0 1 -63 301 -350 140 -21 1 |
| Rev | Accsee docs | A096747 | 1 1 1 1 2 2 1 4 6 6 1 7 18 24 24 1 11 46 96 120 120 1 16 101 326 600 720 720 1 22 197 932 2556 4320 |
| Rev | AccRevsee docs | A349782 | 1 0 1 0 1 2 0 2 5 6 0 6 17 23 24 0 24 74 109 119 120 0 120 394 619 704 719 720 0 720 2484 4108 4843 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 3 0 1 6 2 1 10 11 0 1 15 35 6 1 21 85 50 0 1 28 175 225 24 1 36 322 735 274 0 1 45 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 6 6 0 1 12 33 24 0 1 20 105 200 120 0 1 30 255 900 1370 720 0 1 42 525 2940 8120 |
| 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) | A001710 | 1 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A001710 | 0 0 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^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 |
| 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) | A124380 | 1 1 1 2 4 9 22 57 157 453 1368 4296 13995 47138 163779 585741 2152349 8113188 31326760 123748871 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000774 | 1 2 5 17 74 394 2484 18108 149904 1389456 14257440 160460640 1965444480 26029779840 370643938560 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A121586 | 1 1 3 13 70 446 3276 27252 253296 2602224 29288160 358457760 4740577920 67375532160 1024208720640 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A063039 | 1 1 1 6 66 4200 4192200 5115600 19083776176080 10086416728304192640 126556188275836361347200 |
| 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A065048 | 1 1 1 3 11 50 274 1764 13132 118124 1172700 12753576 150917976 1931559552 26596717056 392156797824 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 1 3 11 35 225 735 6769 22449 269325 902055 13339535 44990231 790943153 2681453775 54631129553 |
| Rev | CentralET(2 n, n) | A187646 | 1 1 11 225 6769 269325 13339535 790943153 54631129553 4308105301929 381922055502195 |
| Rev | CentralOT(2 n + 1, n) | A129505 | 1 3 35 735 22449 902055 44990231 2681453775 185953177553 14710753408923 1307535010540395 |
| 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) | A211210 | 1 1 3 16 115 1021 10696 128472 1734447 25937683 424852351 7554471156 144767131444 2971727661124 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A317274 | 1 -1 -1 2 19 79 76 -2640 -36945 -329371 -1861949 4438774 355714228 7292531180 109844527612 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A067318 | 0 0 1 7 46 326 2556 22212 212976 2239344 25659360 318540960 4261576320 61148511360 937030429440 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A121586 | 1 1 3 13 70 446 3276 27252 253296 2602224 29288160 358457760 4740577920 67375532160 1024208720640 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 1 11 104 984 9764 103340 1172968 14286888 186442992 2600348112 38651163264 610490973312 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 2 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) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | DiagRow2T(n + 2, n) | A000254 | 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Rev | DiagRow3T(n + 3, n) | A000399 | 1 6 35 225 1624 13132 118124 1172700 12753576 150917976 1931559552 26596717056 392156797824 |
| Rev | DiagCol1T(n + 1, 1) | A000217 | 0 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 |
| Rev | DiagCol2T(n + 2, 2) | A000914 | 0 2 11 35 85 175 322 546 870 1320 1925 2717 3731 5005 6580 8500 10812 13566 16815 20615 25025 30107 |
| Rev | DiagCol3T(n + 3, 3) | A001303 | 0 6 50 225 735 1960 4536 9450 18150 32670 55770 91091 143325 218400 323680 468180 662796 920550 |
| Rev | Polysee docs | A256268 | 1 1 1 1 1 1 1 2 1 1 1 6 3 1 1 1 24 15 4 1 1 1 120 105 28 5 1 1 1 720 945 280 45 6 1 1 1 5040 10395 |
| 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 | A000384 | 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225 1326 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A007559 | 1 1 4 28 280 3640 58240 1106560 24344320 608608000 17041024000 528271744000 17961239296000 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A092985 | 1 1 3 28 585 22176 1339975 118514880 14454403425 2326680294400 478015854767451 122087424094272000 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A048993 | 1 0 1 0 -1 1 0 1 -3 1 0 -1 7 -6 1 0 1 -15 25 -10 1 0 -1 31 -90 65 -15 1 0 1 -63 301 -350 140 -21 1 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A106800 | 1 1 0 1 -1 0 1 -3 1 0 1 -6 7 -1 0 1 -10 25 -15 1 0 1 -15 65 -90 31 -1 0 1 -21 140 -350 301 -63 1 0 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A054654 | 1 1 0 1 1 0 1 3 2 0 1 6 11 6 0 1 10 35 50 24 0 1 15 85 225 274 120 0 1 21 175 735 1624 1764 720 0 1 |
| Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 1 -2 -1 0 -1 6 0 1 0 1 -14 11 1 2 0 -1 30 -60 5 -10 -9 0 1 -62 239 -111 29 8 9 0 -1 |
| Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 -2 -1 -1 1 -5 2 1 1 1 -9 16 1 2 2 1 -14 51 -39 -8 -9 -9 1 -20 120 -230 71 8 9 9 1 -27 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 1 1 0 -1 -3 0 1 7 1 0 -1 -15 -6 0 1 31 25 1 0 -1 -63 -90 -10 0 1 127 301 65 1 0 -1 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 2 -9 4 0 -2 21 -24 5 0 2 -45 100 -50 6 0 -2 93 -360 325 -90 7 0 2 -189 1204 -1750 |
| Inv | RowSum∑ k=0..n T(n, k) | A000587 | 1 1 0 -1 1 2 -9 9 50 -267 413 2180 -17731 50533 110176 -1966797 9938669 -8638718 -278475061 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A024430 | 1 0 1 -3 8 -25 97 -434 2095 -10707 58194 -338195 2097933 -13796952 95504749 -692462671 5245040408 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A024429 | 0 1 -1 2 -7 27 -106 443 -2045 10440 -57781 340375 -2115664 13847485 -95394573 690495874 -5235101739 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000110 | 1 -1 2 -5 15 -52 203 -877 4140 -21147 115975 -678570 4213597 -27644437 190899322 -1382958545 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000110 | 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A171367 | 1 0 1 -1 2 -4 9 -22 58 -164 495 -1587 5379 -19195 71872 -281571 1151338 -4902687 21696505 -99598840 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 -2 6 1 -45 113 133 -1990 6310 6249 -162239 767105 -424333 -19563286 150379986 -425333267 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 1 -3 0 13 -27 -32 367 -947 -1354 22091 -85995 -9110 2187149 -13872263 28516056 261197625 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | A063040 | 1 1 1 3 42 150 36270 270900 9440379900 3332912051700 2004302168707167000 1424191116445997823000 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A089026 | 1 1 1 3 1 5 1 7 1 1 1 11 1 13 1 1 1 17 1 19 1 1 1 23 1 1 1 1 1 29 1 31 1 1 1 1 1 37 1 1 1 41 1 43 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | A002870 | 1 1 1 3 7 25 90 350 1701 7770 42525 246730 1379400 9321312 63436373 420693273 3281882604 |
| Inv | ColMiddleT(n, n // 2) | A343279 | 1 0 -1 1 7 -15 -90 301 1701 -7770 -42525 246730 1323652 -9321312 -49329280 408741333 2141764053 |
| Inv | CentralET(2 n, n) | A007820 | 1 -1 7 -90 1701 -42525 1323652 -49329280 2141764053 -106175395755 5917584964655 -366282500870286 |
| Inv | CentralOT(2 n + 1, n) | A247238 | 0 1 -15 301 -7770 246730 -9321312 408741333 -20415995028 1144614626805 -71187132291275 |
| 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) | A343841 | 1 1 -1 -5 15 56 -455 -237 16947 -64220 -529494 6833608 -8606015 -459331677 4335744673 6800310151 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A122455 | 1 1 3 13 71 456 3337 27203 243203 2357356 24554426 272908736 3218032897 40065665043 524575892037 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A101851 | 0 1 1 -2 -1 11 -18 -41 317 -680 -1767 19911 -68264 -59643 2076973 -11905466 18577387 269836343 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 1 -3 0 13 -27 -32 367 -947 -1354 22091 -85995 -9110 2187149 -13872263 28516056 261197625 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A372803 | 0 1 3 -2 -11 31 14 -349 1047 820 -21265 90355 -26352 -2086083 14092615 -32449650 -241320287 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A009235 | 1 1 -1 -1 9 -23 -25 583 -3087 4401 79087 -902097 4783801 2361049 -348382697 4102879415 -24288551071 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A004211 | 1 1 3 11 49 257 1539 10299 75905 609441 5284451 49134923 487026929 5120905441 56878092067 |
| Inv | DiagRow1T(n + 1, n) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
| Inv | DiagRow2T(n + 2, n) | A001296 | 0 1 7 25 65 140 266 462 750 1155 1705 2431 3367 4550 6020 7820 9996 12597 15675 19285 23485 28336 |
| Inv | DiagRow3T(n + 3, n) | A001297 | 0 -1 -15 -90 -350 -1050 -2646 -5880 -11880 -22275 -39325 -66066 -106470 -165620 -249900 -367200 |
| Inv | DiagCol2T(n + 2, 2) | A000225 | 1 -3 7 -15 31 -63 127 -255 511 -1023 2047 -4095 8191 -16383 32767 -65535 131071 -262143 524287 |
| Inv | DiagCol3T(n + 3, 3) | A000392 | 1 -6 25 -90 301 -966 3025 -9330 28501 -86526 261625 -788970 2375101 -7141686 21457825 -64439010 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 -1 2 3 1 0 1 -2 6 4 1 0 2 -6 3 12 5 1 0 -9 14 -21 20 20 6 1 0 9 26 -24 -20 55 |
| 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 | A318765 | 0 -1 -2 3 20 55 114 203 328 495 710 979 1308 1703 2170 2715 3344 4063 4878 5795 6820 7959 9218 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A213170 | 1 2 2 -2 -6 14 26 -178 90 2382 -9446 -13746 287194 -998578 -3687782 56264782 -208446118 -1017677490 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | A309084 | 1 3 6 3 -21 -24 195 111 -3072 4053 57003 -277854 -697539 12261567 -29861778 -371727465 3511027599 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A292866 | 1 1 2 3 -20 -370 -4074 -34293 -138312 2932533 106271090 2192834490 32208497124 206343936097 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A106800 | 1 1 0 1 -1 0 1 -3 1 0 1 -6 7 -1 0 1 -10 25 -15 1 0 1 -15 65 -90 31 -1 0 1 -21 140 -350 301 -63 1 0 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A048993 | 1 0 1 0 -1 1 0 1 -3 1 0 -1 7 -6 1 0 1 -15 25 -10 1 0 -1 31 -90 65 -15 1 0 1 -63 301 -350 140 -21 1 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A132393 | 1 0 1 0 1 1 0 2 3 1 0 6 11 6 1 0 24 50 35 10 1 0 120 274 225 85 15 1 0 720 1764 1624 735 175 21 1 0 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 -2 -1 -1 1 -5 2 1 1 1 -9 16 1 2 2 1 -14 51 -39 -8 -9 -9 1 -20 120 -230 71 8 9 9 1 -27 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 1 -2 -1 0 -1 6 0 1 0 1 -14 11 1 2 0 -1 30 -60 5 -10 -9 0 1 -62 239 -111 29 8 9 0 -1 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -3 0 1 -6 1 1 -10 7 0 1 -15 25 -1 1 -21 65 -15 0 1 -28 140 -90 1 1 -36 266 -350 31 0 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -6 3 0 1 -12 21 -4 0 1 -20 75 -60 5 0 1 -30 195 -360 155 -6 0 1 -42 420 -1400 1505 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000587 | 1 1 0 -1 1 2 -9 9 50 -267 413 2180 -17731 50533 110176 -1966797 9938669 -8638718 -278475061 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A096647 | 1 1 1 2 8 27 97 443 2095 10440 58194 340375 2097933 13847485 95504749 690495874 5245040408 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A096648 | 0 0 -1 -3 -7 -25 -106 -434 -2045 -10707 -57781 -338195 -2115664 -13796952 -95394573 -692462671 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000110 | 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000110 | 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 -2 -4 -2 10 30 24 -88 -332 -312 1196 4932 4552 -22672 -92128 -69032 550920 2055880 839664 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 1 -3 0 13 -27 -32 367 -947 -1354 22091 -85995 -9110 2187149 -13872263 28516056 261197625 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 -2 6 1 -45 113 133 -1990 6310 6249 -162239 767105 -424333 -19563286 150379986 -425333267 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A063040 | 1 1 1 3 42 150 36270 270900 9440379900 3332912051700 2004302168707167000 1424191116445997823000 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A089026 | 1 1 1 3 1 5 1 7 1 1 1 11 1 13 1 1 1 17 1 19 1 1 1 23 1 1 1 1 1 29 1 31 1 1 1 1 1 37 1 1 1 41 1 43 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | A002870 | 1 1 1 3 7 25 90 350 1701 7770 42525 246730 1379400 9321312 63436373 420693273 3281882604 |
| Inv:Rev | ColMiddleT(n, n // 2) | A343278 | 1 1 -1 -3 7 25 -90 -350 1701 6951 -42525 -179487 1323652 5715424 -49329280 -216627840 2141764053 |
| Inv:Rev | CentralET(2 n, n) | A007820 | 1 -1 7 -90 1701 -42525 1323652 -49329280 2141764053 -106175395755 5917584964655 -366282500870286 |
| Inv:Rev | CentralOT(2 n + 1, n) | A129506 | 1 -3 25 -350 6951 -179487 5715424 -216627840 9528822303 -477297033785 26826851689001 |
| 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) | A343841 | 1 1 -1 -5 15 56 -455 -237 16947 -64220 -529494 6833608 -8606015 -459331677 4335744673 6800310151 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A122455 | 1 -1 3 -13 71 -456 3337 -27203 243203 -2357356 24554426 -272908736 3218032897 -40065665043 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -1 -1 5 -1 -36 104 83 -1723 5897 4069 -144508 716572 -534509 -17596489 140441317 -416694549 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 -2 6 1 -45 113 133 -1990 6310 6249 -162239 767105 -424333 -19563286 150379986 -425333267 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 1 13 -29 -94 666 -825 -8567 55375 -83907 -941280 8004712 -22468133 -117814995 1708502593 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A213170 | 1 2 2 -2 -6 14 26 -178 90 2382 -9446 -13746 287194 -998578 -3687782 56264782 -208446118 -1017677490 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001861 | 1 -2 6 -22 94 -454 2430 -14214 89918 -610182 4412798 -33827974 273646526 -2326980998 20732504062 |
| Inv:Rev | DiagRow2T(n + 2, n) | A000225 | 1 -3 7 -15 31 -63 127 -255 511 -1023 2047 -4095 8191 -16383 32767 -65535 131071 -262143 524287 |
| Inv:Rev | DiagRow3T(n + 3, n) | A000392 | 1 -6 25 -90 301 -966 3025 -9330 28501 -86526 261625 -788970 2375101 -7141686 21457825 -64439010 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A001296 | 0 1 7 25 65 140 266 462 750 1155 1705 2431 3367 4550 6020 7820 9996 12597 15675 19285 23485 28336 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A001297 | 0 -1 -15 -90 -350 -1050 -2646 -5880 -11880 -22275 -39325 -66066 -106470 -165620 -249900 -367200 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 -1 -1 1 1 1 1 -1 -2 1 1 1 2 9 1 -3 1 1 1 -9 -23 19 5 -4 1 1 1 9 -25 -128 25 |
| 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 | A028387 | 1 -1 -1 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A009235 | 1 1 -1 -1 9 -23 -25 583 -3087 4401 79087 -902097 4783801 2361049 -348382697 4102879415 -24288551071 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A317996 | 1 1 -2 1 19 -128 379 1549 -32600 261631 -845909 -10713602 237695149 -2513395259 11792378662 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A318183 | 1 1 -1 1 25 -674 15211 -331827 5987745 15901597 -13125035449 1292056076070 -103145930581319 |
| << | 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.