OEIS Similars: A137452, A061356, A139526
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A137452 | 1 0 1 0 2 1 0 9 6 1 0 64 48 12 1 0 625 500 150 20 1 0 7776 6480 2160 360 30 1 0 117649 100842 36015 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 6 9 0 1 12 48 64 0 1 20 150 500 625 0 1 30 360 2160 6480 7776 0 1 42 735 6860 36015 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A059297 | 1 0 1 0 -2 1 0 3 -6 1 0 -4 24 -12 1 0 5 -80 90 -20 1 0 -6 240 -540 240 -30 1 0 7 -672 2835 -2240 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A059299 | 1 1 0 1 -2 0 1 -6 3 0 1 -12 24 -4 0 1 -20 90 -80 5 0 1 -30 240 -540 240 -6 0 1 -42 525 -2240 2835 |
| Std | Accsee docs | missing | 1 0 1 0 2 3 0 9 15 16 0 64 112 124 125 0 625 1125 1275 1295 1296 0 7776 14256 16416 16776 16806 |
| Std | AccRevsee docs | missing | 1 1 1 1 3 3 1 7 16 16 1 13 61 125 125 1 21 171 671 1296 1296 1 31 391 2551 9031 16807 16807 1 43 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 2 0 9 1 0 64 6 0 625 48 1 0 7776 500 12 0 117649 6480 150 1 0 2097152 100842 2160 20 0 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 4 3 0 18 18 4 0 128 144 48 5 0 1250 1500 600 100 6 0 15552 19440 8640 1800 180 7 0 235298 |
| Std | RowSum∑ k=0..n T(n, k) | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A274278 | 1 0 1 6 49 520 6841 107744 1979713 41611392 985263601 25958682112 753424361713 23888905963520 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A195136 | 0 1 2 10 76 776 9966 154400 2803256 58388608 1372684090 35958682112 1038736032324 32805006411776 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000312 | 1 -1 -1 -4 -27 -256 -3125 -46656 -823543 -16777216 -387420489 -10000000000 -285311670611 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 2 10 70 674 8288 124280 2200174 44918105 1038958770 26852449045 766951172304 23988906739205 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 5 40 425 5616 88837 1638400 34543665 820000000 21650246981 629493202944 19989481318105 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A367255 | 1 2 7 40 325 3456 45619 720896 13286025 280000000 6645125311 175432531968 5100764198413 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 18 192 7500 38880 7058940 220200960 12053081880 63000000000 65362309994520 286058222714880 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | A000169 | 1 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 2 9 48 500 2160 36015 143360 3306744 12600000 372027810 1379524608 49696825464 180889572864 |
| Std | CentralET(2 n, n) | A367254 | 1 2 48 2160 143360 12600000 1379524608 180889572864 27638114549760 4822114348846080 |
| Std | CentralOT(2 n + 1, n) | missing | 0 9 500 36015 3306744 372027810 49696825464 7696360546875 1356645307125680 268283197308856158 |
| 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) | A367256 | 1 1 5 46 593 9726 192637 4457580 117769409 3492894070 114790042901 4137157889316 162154385331985 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367257 | 1 1 -3 10 -15 -474 12565 -258572 5136705 -102255290 2019481101 -37521627252 543274535089 |
| Std | TransNat0∑ k=0..n T(n, k) k | A089946 | 0 1 4 24 200 2160 28812 458752 8503056 180000000 4287177620 113515167744 3308603804376 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A367255 | 1 2 7 40 325 3456 45619 720896 13286025 280000000 6645125311 175432531968 5100764198413 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A225497 | 0 1 6 42 380 4320 59682 974848 18423288 396000000 9548713790 255409127424 7507985556084 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A052750 | 1 1 5 49 729 14641 371293 11390625 410338673 16983563041 794280046581 41426511213649 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A085527 | 1 1 -3 25 -343 6561 -161051 4826809 -170859375 6975757441 -322687697779 16679880978201 |
| Std | DiagRow1T(n + 1, n) | 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 | DiagRow2T(n + 2, n) | missing | 0 9 48 150 360 735 1344 2268 3600 5445 7920 11154 15288 20475 26880 34680 44064 55233 68400 83790 |
| Std | DiagRow3T(n + 3, n) | missing | 0 64 500 2160 6860 17920 40824 84000 159720 285120 483340 784784 1228500 1863680 2751280 3965760 |
| Std | DiagCol1T(n + 1, 1) | A000169 | 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Std | DiagCol2T(n + 2, 2) | A053506 | 1 6 48 500 6480 100842 1835008 38263752 900000000 23579476910 681091006464 21505924728444 |
| Std | DiagCol3T(n + 3, 3) | A053507 | 1 12 150 2160 36015 688128 14880348 360000000 9646149645 283787919360 9098660462034 315866083233792 |
| Std | Polysee docs | A232006 | 1 0 1 0 1 1 0 3 2 1 0 16 8 3 1 0 125 50 15 4 1 0 1296 432 108 24 5 1 0 16807 4802 1029 196 35 6 1 0 |
| 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 | A005563 | 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 16 50 108 196 320 486 700 968 1296 1690 2156 2700 3328 4046 4860 5776 6800 7938 9196 10580 12096 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A007334 | 1 2 8 50 432 4802 65536 1062882 20000000 428717762 10319560704 275716983698 8099130339328 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A362354 | 1 3 15 108 1029 12288 177147 3000000 58461513 1289945088 31813498119 867763964928 25949267578125 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A193678 | 1 1 8 108 2048 50000 1492992 52706752 2147483648 99179645184 5120000000000 292159150705664 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A137452 | 1 0 -1 0 -2 1 0 -9 6 -1 0 -64 48 -12 1 0 -625 500 -150 20 -1 0 -7776 6480 -2160 360 -30 1 0 -117649 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 0 1 -2 0 -1 6 -9 0 1 -12 48 -64 0 -1 20 -150 500 -625 0 1 -30 360 -2160 6480 -7776 0 -1 42 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 2 1 0 -3 -6 1 0 -68 -120 12 1 0 535 1000 -90 -20 1 0 28866 53760 -4860 -960 30 1 0 -544747 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 -6 -3 0 1 12 -120 -68 0 1 -20 -90 1000 535 0 1 30 -960 -4860 53760 28866 0 1 -42 -525 |
| Alt | Accsee docs | missing | 1 0 -1 0 -2 -1 0 -9 -3 -4 0 -64 -16 -28 -27 0 -625 -125 -275 -255 -256 0 -7776 -1296 -3456 -3096 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 -1 -1 -1 5 -4 -4 1 -11 37 -27 -27 -1 19 -131 369 -256 -256 1 -29 331 -1829 4651 -3125 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -2 0 -9 1 0 -64 6 0 -625 48 -1 0 -7776 500 -12 0 -117649 6480 -150 1 0 -2097152 100842 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -4 3 0 -18 18 -4 0 -128 144 -48 5 0 -1250 1500 -600 100 -6 0 -15552 19440 -8640 1800 -180 |
| Alt | RowSum∑ k=0..n T(n, k) | A000312 | 1 -1 -1 -4 -27 -256 -3125 -46656 -823543 -16777216 -387420489 -10000000000 -285311670611 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A274278 | 1 0 1 6 49 520 6841 107744 1979713 41611392 985263601 25958682112 753424361713 23888905963520 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A195136 | 0 -1 -2 -10 -76 -776 -9966 -154400 -2803256 -58388608 -1372684090 -35958682112 -1038736032324 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -2 -8 -58 -578 -7288 -111318 -1998450 -41247369 -962417546 -25052162323 -719785604912 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -3 -16 -135 -1536 -21875 -373248 -7411887 -167772160 -4261625379 -120000000000 -3709051717943 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000312 | 1 -2 -1 -4 -27 -256 -3125 -46656 -823543 -16777216 -387420489 -10000000000 -285311670611 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 18 192 7500 38880 7058940 220200960 12053081880 63000000000 65362309994520 286058222714880 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A000169 | 1 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -2 -9 48 500 -2160 -36015 143360 3306744 -12600000 -372027810 1379524608 49696825464 |
| Alt | CentralET(2 n, n) | A367254 | 1 -2 48 -2160 143360 -12600000 1379524608 -180889572864 27638114549760 -4822114348846080 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -9 500 -36015 3306744 -372027810 49696825464 -7696360546875 1356645307125680 -268283197308856158 |
| 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) | A367257 | 1 -1 -3 -10 -15 474 12565 258572 5136705 102255290 2019481101 37521627252 543274535089 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367256 | 1 -1 5 -46 593 -9726 192637 -4457580 117769409 -3492894070 114790042901 -4137157889316 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 -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 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000312 | 1 -2 -1 -4 -27 -256 -3125 -46656 -823543 -16777216 -387420489 -10000000000 -285311670611 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A055541 | 0 -1 2 6 36 320 3750 54432 941192 18874368 430467210 11000000000 311249095212 9659108818944 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A085527 | 1 -1 -3 -25 -343 -6561 -161051 -4826809 -170859375 -6975757441 -322687697779 -16679880978201 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A052750 | 1 -1 5 -49 729 -14641 371293 -11390625 410338673 -16983563041 794280046581 -41426511213649 |
| Alt | DiagRow1T(n + 1, n) | 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 |
| Alt | DiagRow2T(n + 2, n) | missing | 0 -9 48 -150 360 -735 1344 -2268 3600 -5445 7920 -11154 15288 -20475 26880 -34680 44064 -55233 |
| Alt | DiagRow3T(n + 3, n) | missing | 0 -64 500 -2160 6860 -17920 40824 -84000 159720 -285120 483340 -784784 1228500 -1863680 2751280 |
| Alt | DiagCol1T(n + 1, 1) | A000169 | -1 -2 -9 -64 -625 -7776 -117649 -2097152 -43046721 -1000000000 -25937424601 -743008370688 |
| Alt | DiagCol2T(n + 2, 2) | A053506 | 1 6 48 500 6480 100842 1835008 38263752 900000000 23579476910 681091006464 21505924728444 |
| Alt | DiagCol3T(n + 3, 3) | A053507 | -1 -12 -150 -2160 -36015 -688128 -14880348 -360000000 -9646149645 -283787919360 -9098660462034 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 -1 -2 1 0 -4 0 -3 1 0 -27 -2 3 -4 1 0 -256 -16 0 8 -5 1 0 -3125 -162 -3 -4 15 -6 1 0 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A366151 | 0 -4 -2 0 -4 -20 -54 -112 -200 -324 -490 -704 -972 -1300 -1694 -2160 -2704 -3332 -4050 -4864 -5780 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 0 -2 -16 -162 -2048 -31250 -559872 -11529602 -268435456 -6973568802 -200000000000 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 3 0 -3 -48 -729 -12288 -234375 -5038848 -121060821 -3221225472 -94143178827 -3000000000000 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 6 9 0 1 12 48 64 0 1 20 150 500 625 0 1 30 360 2160 6480 7776 0 1 42 735 6860 36015 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A059297 | 1 0 1 0 -2 1 0 3 -6 1 0 -4 24 -12 1 0 5 -80 90 -20 1 0 -6 240 -540 240 -30 1 0 7 -672 2835 -2240 |
| Rev | Accsee docs | missing | 1 1 1 1 3 3 1 7 16 16 1 13 61 125 125 1 21 171 671 1296 1296 1 31 391 2551 9031 16807 16807 1 43 |
| Rev | AccRevsee docs | missing | 1 0 1 0 2 3 0 9 15 16 0 64 112 124 125 0 625 1125 1275 1295 1296 0 7776 14256 16416 16776 16806 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 2 1 6 0 1 12 9 1 20 48 0 1 30 150 64 1 42 360 500 0 1 56 735 2160 625 1 72 1344 6860 6480 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 4 0 1 12 27 0 1 24 144 256 0 1 40 450 2000 3125 0 1 60 1080 8640 32400 46656 0 1 84 2205 |
| Rev | RowSum∑ k=0..n T(n, k) | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 10 49 776 6841 154400 1979713 58388608 985263601 35958682112 753424361713 32805006411776 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 2 6 76 520 9966 107744 2803256 41611392 1372684090 25958682112 1038736032324 23888905963520 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000312 | 1 1 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000272 | 1 1 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 3 7 22 69 245 903 3577 14757 64070 288737 1354625 6569549 32948567 170190323 904978110 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A367255 | 1 2 7 40 325 3456 45619 720896 13286025 280000000 6645125311 175432531968 5100764198413 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 5 40 425 5616 88837 1638400 34543665 820000000 21650246981 629493202944 19989481318105 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 18 192 7500 38880 7058940 220200960 12053081880 63000000000 65362309994520 286058222714880 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A000169 | 1 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 6 48 150 2160 6860 143360 459270 12600000 40584852 1379524608 4459971516 180889572864 |
| Rev | CentralET(2 n, n) | A367254 | 1 2 48 2160 143360 12600000 1379524608 180889572864 27638114549760 4822114348846080 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 6 150 6860 459270 40584852 4459971516 586389375000 89777998265670 15689075866014980 |
| 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) | A367256 | 1 1 5 46 593 9726 192637 4457580 117769409 3492894070 114790042901 4137157889316 162154385331985 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367257 | 1 -1 -3 -10 -15 474 12565 258572 5136705 102255290 2019481101 37521627252 543274535089 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A065513 | 0 0 2 24 300 4320 72030 1376256 29760696 720000000 19292299290 567575838720 18197320924068 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 5 40 425 5616 88837 1638400 34543665 820000000 21650246981 629493202944 19989481318105 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 2 42 780 15120 318990 7397376 188484408 5256000000 159599930490 5250076508160 186172590992388 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A007334 | 1 2 8 50 432 4802 65536 1062882 20000000 428717762 10319560704 275716983698 8099130339328 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 0 -2 -16 -162 -2048 -31250 -559872 -11529602 -268435456 -6973568802 -200000000000 |
| Rev | DiagRow1T(n + 1, n) | A000169 | 1 2 9 64 625 7776 117649 2097152 43046721 1000000000 25937424601 743008370688 23298085122481 |
| Rev | DiagRow2T(n + 2, n) | A053506 | 1 6 48 500 6480 100842 1835008 38263752 900000000 23579476910 681091006464 21505924728444 |
| Rev | DiagRow3T(n + 3, n) | A053507 | 1 12 150 2160 36015 688128 14880348 360000000 9646149645 283787919360 9098660462034 315866083233792 |
| Rev | DiagCol1T(n + 1, 1) | 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 |
| Rev | DiagCol2T(n + 2, 2) | missing | 0 9 48 150 360 735 1344 2268 3600 5445 7920 11154 15288 20475 26880 34680 44064 55233 68400 83790 |
| Rev | DiagCol3T(n + 3, 3) | missing | 0 64 500 2160 6860 17920 40824 84000 159720 285120 483340 784784 1228500 1863680 2751280 3965760 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 3 1 1 1 16 5 1 1 1 125 49 7 1 1 1 1296 729 100 9 1 1 1 16807 14641 2197 169 11 1 1 1 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A016778 | 1 16 49 100 169 256 361 484 625 784 961 1156 1369 1600 1849 2116 2401 2704 3025 3364 3721 4096 4489 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A052750 | 1 1 5 49 729 14641 371293 11390625 410338673 16983563041 794280046581 41426511213649 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A052752 | 1 1 7 100 2197 65536 2476099 113379904 6103515625 377801998336 26439622160671 2064377754059776 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 100 4913 456976 69343957 15625000000 4902227890625 2044140858654976 1093685272684360901 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A059297 | 1 0 1 0 -2 1 0 3 -6 1 0 -4 24 -12 1 0 5 -80 90 -20 1 0 -6 240 -540 240 -30 1 0 7 -672 2835 -2240 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A059299 | 1 1 0 1 -2 0 1 -6 3 0 1 -12 24 -4 0 1 -20 90 -80 5 0 1 -30 240 -540 240 -6 0 1 -42 525 -2240 2835 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 6 9 0 1 12 48 64 0 1 20 150 500 625 0 1 30 360 2160 6480 7776 0 1 42 735 6860 36015 |
| Inv | Accsee docs | missing | 1 0 1 0 -2 -1 0 3 -3 -2 0 -4 20 8 9 0 5 -75 15 -5 -4 0 -6 234 -306 -66 -96 -95 0 7 -665 2170 -70 |
| Inv | AccRevsee docs | missing | 1 1 1 1 -1 -1 1 -5 -2 -2 1 -11 13 9 9 1 -19 71 -9 -4 -4 1 -29 211 -329 -89 -95 -95 1 -41 484 -1756 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -2 0 3 1 0 -4 -6 0 5 24 1 0 -6 -80 -12 0 7 240 90 1 0 -8 -672 -540 -20 0 9 1792 2835 240 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -4 3 0 6 -18 4 0 -8 72 -48 5 0 10 -240 360 -100 6 0 -12 720 -2160 1200 -180 7 0 14 -2016 |
| Inv | RowSum∑ k=0..n T(n, k) | A003725 | 1 1 -1 -2 9 -4 -95 414 49 -10088 55521 -13870 -2024759 15787188 -28612415 -616876274 7476967905 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A009121 | 1 0 1 -6 25 -100 481 -2954 20721 -151848 1146721 -9111982 77652169 -710421452 6891125697 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A009565 | 0 1 -2 4 -16 96 -576 3368 -20672 141760 -1091200 9098112 -79676928 726208640 -6919738112 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000248 | 1 -1 3 -10 41 -196 1057 -6322 41393 -293608 2237921 -18210094 157329097 -1436630092 13810863809 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A360814 | 1 0 1 -2 4 -10 30 -98 338 -1240 4877 -20496 91213 -426678 2090081 -10702438 57193760 -318283388 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -3 -2 33 -64 -335 2724 -4655 -55952 504801 -1179100 -14176679 173674632 -691456415 -4550929124 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 -1 -8 21 36 -425 1002 5145 -55016 161451 998790 -14169947 63133188 233657775 -5935967534 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 24 720 2160 907200 108864000 137168640000 57610828800000 266162029056000000 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 24 90 540 2835 17920 129024 860160 7218750 61875000 502734375 5043886848 50438868480 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -2 3 24 -80 -540 2835 17920 -129024 -787500 7218750 43110144 -480370176 -2826399576 37096494435 |
| Inv | CentralET(2 n, n) | A367271 | 1 -2 24 -540 17920 -787500 43110144 -2826399576 215922769920 -18836384175180 1847560000000000 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 3 -80 2835 -129024 7218750 -480370176 37096494435 -3262832967680 322102169395578 |
| 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) | A367273 | 1 1 -3 -8 81 26 -3815 17494 178241 -2817746 3552201 315952418 -3635118575 -11060115936 782886068497 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367272 | 1 1 5 28 209 1826 18217 203106 2487361 33077566 473318201 7234847126 117435618577 2014339775800 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 -6 12 40 -330 588 5096 -44928 105930 1012660 -12145188 47346000 262270190 -5319091260 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 -1 -8 21 36 -425 1002 5145 -55016 161451 998790 -14169947 63133188 233657775 -5935967534 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 -12 0 200 -780 -1344 30016 -134208 -282780 8028680 -49398096 -26677248 3298301188 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A356819 | 1 1 -3 1 41 -239 229 8401 -87151 324577 3238541 -70271519 601086265 -142860431 -81504662539 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A216689 | 1 1 5 25 153 1121 9373 87417 898033 10052353 121492341 1573957529 21729801481 318121178337 |
| Inv | DiagRow1T(n + 1, n) | A002378 | 0 -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 |
| Inv | DiagRow2T(n + 2, n) | missing | 0 3 24 90 240 525 1008 1764 2880 4455 6600 9438 13104 17745 23520 30600 39168 49419 61560 75810 |
| Inv | DiagRow3T(n + 3, n) | missing | 0 -4 -80 -540 -2240 -7000 -18144 -41160 -84480 -160380 -286000 -484484 -786240 -1230320 -1865920 |
| Inv | DiagCol1T(n + 1, 1) | A000027 | 1 -2 3 -4 5 -6 7 -8 9 -10 11 -12 13 -14 15 -16 17 -18 19 -20 21 -22 23 -24 25 -26 27 -28 29 -30 31 |
| 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) | A036216 | 1 -12 90 -540 2835 -13608 61236 -262440 1082565 -4330260 16888014 -64481508 241805655 -892820880 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 -1 2 1 0 -2 0 3 1 0 9 -10 3 4 1 0 -4 8 -18 8 5 1 0 -95 122 -39 -20 15 6 1 0 414 -428 |
| 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 | 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 -2 -10 -18 -20 -10 18 70 152 270 430 638 900 1222 1610 2070 2608 3230 3942 4750 5660 6678 7810 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 0 -10 8 122 -428 -1594 18608 -26254 -648916 5081342 3318856 -347739286 2495737220 6457268918 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 3 -18 -39 348 441 -11778 18129 475416 -3100791 -13831518 304225785 -884361228 -21201487431 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 0 -18 -144 -100 16380 267246 749504 -69401448 -1849688100 -11405686270 797088487536 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A059299 | 1 1 0 1 -2 0 1 -6 3 0 1 -12 24 -4 0 1 -20 90 -80 5 0 1 -30 240 -540 240 -6 0 1 -42 525 -2240 2835 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A059297 | 1 0 1 0 -2 1 0 3 -6 1 0 -4 24 -12 1 0 5 -80 90 -20 1 0 -6 240 -540 240 -30 1 0 7 -672 2835 -2240 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A137452 | 1 0 1 0 2 1 0 9 6 1 0 64 48 12 1 0 625 500 150 20 1 0 7776 6480 2160 360 30 1 0 117649 100842 36015 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 -1 -1 1 -5 -2 -2 1 -11 13 9 9 1 -19 71 -9 -4 -4 1 -29 211 -329 -89 -95 -95 1 -41 484 -1756 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -2 -1 0 3 -3 -2 0 -4 20 8 9 0 5 -75 15 -5 -4 0 -6 234 -306 -66 -96 -95 0 7 -665 2170 -70 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -2 1 -6 0 1 -12 3 1 -20 24 0 1 -30 90 -4 1 -42 240 -80 0 1 -56 525 -540 5 1 -72 1008 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -4 0 1 -12 9 0 1 -24 72 -16 0 1 -40 270 -320 25 0 1 -60 720 -2160 1200 -36 0 1 -84 1575 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A003725 | 1 1 -1 -2 9 -4 -95 414 49 -10088 55521 -13870 -2024759 15787188 -28612415 -616876274 7476967905 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A195509 | 1 1 1 4 25 96 481 3368 20721 141760 1146721 9098112 77652169 726208640 6891125697 69344336896 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -2 -6 -16 -100 -576 -2954 -20672 -151848 -1091200 -9111982 -79676928 -710421452 -6919738112 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000248 | 1 1 3 10 41 196 1057 6322 41393 293608 2237921 18210094 157329097 1436630092 13810863809 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 -1 -5 -8 5 57 119 -65 -1063 -2496 1875 28313 66893 -85065 -982545 -2130688 4789537 41662081 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 -1 -8 21 36 -425 1002 5145 -55016 161451 998790 -14169947 63133188 233657775 -5935967534 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -3 -2 33 -64 -335 2724 -4655 -55952 504801 -1179100 -14176679 173674632 -691456415 -4550929124 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 6 24 720 2160 907200 108864000 137168640000 57610828800000 266162029056000000 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000027 | 1 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:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 24 90 540 2835 17920 129024 860160 7218750 61875000 502734375 5043886848 50438868480 |
| Inv:Rev | ColMiddleT(n, n // 2) | A367274 | 1 1 -2 -6 24 90 -540 -2240 17920 78750 -787500 -3592512 43110144 201885684 -2826399576 -13495173120 |
| Inv:Rev | CentralET(2 n, n) | A367271 | 1 -2 24 -540 17920 -787500 43110144 -2826399576 215922769920 -18836384175180 1847560000000000 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -6 90 -2240 78750 -3592512 201885684 -13495173120 1046465787510 -92378000000000 9148544655566316 |
| 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) | A367273 | 1 1 -3 -8 81 26 -3815 17494 178241 -2817746 3552201 315952418 -3635118575 -11060115936 782886068497 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A367272 | 1 -1 5 -28 209 -1826 18217 -203106 2487361 -33077566 473318201 -7234847126 117435618577 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -2 0 24 -60 -240 2310 -4704 -45864 449280 -1165230 -12151920 157887444 -662844000 -3934052850 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -3 -2 33 -64 -335 2724 -4655 -55952 504801 -1179100 -14176679 173674632 -691456415 -4550929124 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -2 6 48 -300 -240 10710 -48384 -142632 3150720 -15928110 -49478880 1410361524 -9653297472 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 0 -10 8 122 -428 -1594 18608 -26254 -648916 5081342 3318856 -347739286 2495737220 6457268918 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A275707 | 1 -2 8 -38 216 -1402 10156 -80838 698704 -6498674 64579284 -681642238 7605025720 -89318058858 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000027 | 1 -2 3 -4 5 -6 7 -8 9 -10 11 -12 13 -14 15 -16 17 -18 19 -20 21 -22 23 -24 25 -26 27 -28 29 -30 31 |
| 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) | A036216 | 1 -12 90 -540 2835 -13608 61236 -262440 1082565 -4330260 16888014 -64481508 241805655 -892820880 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A002378 | 0 -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 |
| Inv:Rev | DiagCol2T(n + 2, 2) | missing | 0 3 24 90 240 525 1008 1764 2880 4455 6600 9438 13104 17745 23520 30600 39168 49419 61560 75810 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | 0 -4 -80 -540 -2240 -7000 -18144 -41160 -84480 -160380 -286000 -484484 -786240 -1230320 -1865920 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 -1 1 1 1 -2 -3 1 1 1 9 1 -5 1 1 1 -4 41 10 -7 1 1 1 -95 -239 73 25 -9 1 1 1 414 229 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A100536 | 1 -2 1 10 25 46 73 106 145 190 241 298 361 430 505 586 673 766 865 970 1081 1198 1321 1450 1585 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A356819 | 1 1 -3 1 41 -239 229 8401 -87151 324577 3238541 -70271519 601086265 -142860431 -81504662539 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A356820 | 1 1 -5 10 73 -1004 5473 15562 -746447 9174088 -41916959 -823985546 24629093641 -335144105828 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A320258 | 1 1 -3 10 81 -4724 156205 -4406814 76958273 3775676248 -698309272899 72802616429830 |
| << | 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.