OEIS Similars: A022166
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A022166 | 1 1 1 1 3 1 1 7 7 1 1 15 35 15 1 1 31 155 155 31 1 1 63 651 1395 651 63 1 1 127 2667 11811 11811 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A022166 | 1 1 1 1 3 1 1 7 7 1 1 15 35 15 1 1 31 155 155 31 1 1 63 651 1395 651 63 1 1 127 2667 11811 11811 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A135950 | 1 -1 1 2 -3 1 -8 14 -7 1 64 -120 70 -15 1 -1024 1984 -1240 310 -31 1 32768 -64512 41664 -11160 1302 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A158474 | 1 1 -1 1 -3 2 1 -7 14 -8 1 -15 70 -120 64 1 -31 310 -1240 1984 -1024 1 -63 1302 -11160 41664 -64512 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A135950 | 1 -1 1 2 -3 1 -8 14 -7 1 64 -120 70 -15 1 -1024 1984 -1240 310 -31 1 32768 -64512 41664 -11160 1302 |
| Std | Accsee docs | missing | 1 1 2 1 4 5 1 8 15 16 1 16 51 66 67 1 32 187 342 373 374 1 64 715 2110 2761 2824 2825 1 128 2795 |
| Std | AccRevsee docs | missing | 1 1 2 1 4 5 1 8 15 16 1 16 51 66 67 1 32 187 342 373 374 1 64 715 2110 2761 2824 2825 1 128 2795 |
| Std | AntiDiagsee docs | missing | 1 1 1 1 1 3 1 7 1 1 15 7 1 31 35 1 1 63 155 15 1 127 651 155 1 1 255 2667 1395 31 1 511 10795 11811 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 6 3 1 14 21 4 1 30 105 60 5 1 62 465 620 155 6 1 126 1953 5580 3255 378 7 1 254 8001 47244 |
| Std | RowSum∑ k=0..n T(n, k) | A006116 | 1 2 5 16 67 374 2825 29212 417199 8283458 229755605 8933488744 488176700923 37558989808526 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A289541 | 1 1 2 8 37 187 1304 14606 222379 4141729 107836478 4466744372 258501941713 18779494904263 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 3 8 30 187 1521 14606 194820 4141729 121919127 4466744372 229674759210 18779494904263 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A290974 | 1 0 -1 0 7 0 -217 0 27559 0 -14082649 0 28827182503 0 -236123451882073 0 7737057147819885991 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A006116 | 1 2 5 16 67 374 2825 29212 417199 8283458 229755605 8933488744 488176700923 37558989808526 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 4 9 23 68 234 935 4349 23770 153488 1167789 10456867 110822848 1395804342 20827928659 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 10 40 201 1309 11300 131454 2085995 45559019 1378533630 58067676836 3417236906461 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 10 40 201 1309 11300 131454 2085995 45559019 1378533630 58067676836 3417236906461 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 7 105 155 9765 82677 3011805 16548735 16929355905 110013941389 450507089987955 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A019320 | 1 1 3 7 5 31 3 127 17 73 11 2047 13 8191 43 151 257 131071 57 524287 205 2359 683 8388607 241 |
| Std | RowMaxMax k=0..n | T(n, k) | | A006099 | 1 1 3 7 35 155 1395 11811 200787 3309747 109221651 3548836819 230674393235 14877590196755 |
| Std | ColMiddleT(n, n // 2) | A006099 | 1 1 3 7 35 155 1395 11811 200787 3309747 109221651 3548836819 230674393235 14877590196755 |
| Std | CentralET(2 n, n) | A006098 | 1 3 35 1395 200787 109221651 230674393235 1919209135381395 63379954960524853651 |
| Std | CentralOT(2 n + 1, n) | A218449 | 1 7 155 11811 3309747 3548836819 14877590196755 246614610741341843 16256896431763117598611 |
| Std | 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 |
| Std | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 8 44 332 3412 48188 940564 25545052 969582644 51635485244 3867743513812 408350633776412 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 0 92 0 -9124 0 3774172 0 -6459170980 0 45480123143132 0 -1310657322035590052 0 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 5 24 134 935 8475 102242 1668796 37275561 1148778025 49134188092 2929060205538 244133433755419 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 10 40 201 1309 11300 131454 2085995 45559019 1378533630 58067676836 3417236906461 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 7 44 306 2567 27249 377366 6960476 173496553 5905329123 276564718960 17921946975414 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A182176 | 1 3 11 51 307 2451 26387 387987 7866259 221472147 8703733139 479243212179 37070813107603 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 -1 7 7 -217 -217 27559 27559 -14082649 -14082649 28827182503 28827182503 -236123451882073 |
| Std | DiagRow1T(n + 1, n) | A000225 | 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535 131071 262143 524287 1048575 |
| Std | DiagRow2T(n + 2, n) | A006095 | 1 7 35 155 651 2667 10795 43435 174251 698027 2794155 11180715 44731051 178940587 715795115 |
| Std | DiagRow3T(n + 3, n) | A006096 | 1 15 155 1395 11811 97155 788035 6347715 50955971 408345795 3269560515 26167664835 209386049731 |
| Std | DiagCol1T(n + 1, 1) | A000225 | 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535 131071 262143 524287 1048575 |
| Std | DiagCol2T(n + 2, 2) | A006095 | 1 7 35 155 651 2667 10795 43435 174251 698027 2794155 11180715 44731051 178940587 715795115 |
| Std | DiagCol3T(n + 3, 3) | A006096 | 1 15 155 1395 11811 97155 788035 6347715 50955971 408345795 3269560515 26167664835 209386049731 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 16 11 4 1 1 67 51 19 5 1 1 374 307 112 29 6 1 1 2825 2451 847 205 41 7 1 1 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A028387 | 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 701 755 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 16 51 112 205 336 511 736 1017 1360 1771 2256 2821 3472 4215 5056 6001 7056 8227 9520 10941 12496 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A182176 | 1 3 11 51 307 2451 26387 387987 7866259 221472147 8703733139 479243212179 37070813107603 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 19 112 847 8428 112483 2042824 51027319 1766869636 85292358571 5763692347168 546835143373183 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 11 112 1837 45906 1705375 93130192 7437830329 866657162890 147145207120331 36374221860116064 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A022166 | 1 1 -1 1 -3 1 1 -7 7 -1 1 -15 35 -15 1 1 -31 155 -155 31 -1 1 -63 651 -1395 651 -63 1 1 -127 2667 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A022166 | 1 -1 1 1 -3 1 -1 7 -7 1 1 -15 35 -15 1 -1 31 -155 155 -31 1 1 -63 651 -1395 651 -63 1 -1 127 -2667 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -4 3 1 20 -14 -7 1 424 -300 -140 15 1 -9456 6696 3100 -310 -31 1 -841312 595728 276024 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 3 -4 1 -7 -14 20 1 15 -140 -300 424 1 -31 -310 3100 6696 -9456 1 63 -2604 -27900 276024 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A135950 | 1 1 1 2 3 1 8 14 7 1 64 120 70 15 1 1024 1984 1240 310 31 1 32768 64512 41664 11160 1302 63 1 |
| Alt | Accsee docs | missing | 1 1 0 1 -2 -1 1 -6 1 0 1 -14 21 6 7 1 -30 125 -30 1 0 1 -62 589 -806 -155 -218 -217 1 -126 2541 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -2 -1 -1 6 -1 0 1 -14 21 6 7 -1 30 -125 30 -1 0 1 -62 589 -806 -155 -218 -217 -1 126 -2541 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -1 1 -3 1 -7 1 1 -15 7 1 -31 35 -1 1 -63 155 -15 1 -127 651 -155 1 1 -255 2667 -1395 31 1 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -6 3 1 -14 21 -4 1 -30 105 -60 5 1 -62 465 -620 155 -6 1 -126 1953 -5580 3255 -378 7 1 |
| Alt | RowSum∑ k=0..n T(n, k) | A290974 | 1 0 -1 0 7 0 -217 0 27559 0 -14082649 0 28827182503 0 -236123451882073 0 7737057147819885991 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A289541 | 1 1 2 8 37 187 1304 14606 222379 4141729 107836478 4466744372 258501941713 18779494904263 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -3 -8 -30 -187 -1521 -14606 -194820 -4141729 -121919127 -4466744372 -229674759210 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A006116 | 1 2 5 16 67 374 2825 29212 417199 8283458 229755605 8933488744 488176700923 37558989808526 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A006116 | 1 2 5 16 67 374 2825 29212 417199 8283458 229755605 8933488744 488176700923 37558989808526 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -2 -5 -7 4 78 371 1049 -876 -42994 -417709 -2441063 2275028 360636174 7190981587 86108697241 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -2 -4 21 67 -868 -4438 137795 1159249 -84495894 -1199994376 201790277521 4942804152223 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -2 4 21 -67 -868 4438 137795 -1159249 -84495894 1199994376 201790277521 -4942804152223 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 3 7 105 155 9765 82677 3011805 16548735 16929355905 110013941389 450507089987955 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A019320 | 1 1 3 7 5 31 3 127 17 73 11 2047 13 8191 43 151 257 131071 57 524287 205 2359 683 8388607 241 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A006099 | 1 1 3 7 35 155 1395 11811 200787 3309747 109221651 3548836819 230674393235 14877590196755 |
| Alt | ColMiddleT(n, n // 2) | A006099 | 1 1 -3 -7 35 155 -1395 -11811 200787 3309747 -109221651 -3548836819 230674393235 14877590196755 |
| Alt | CentralET(2 n, n) | A006098 | 1 -3 35 -1395 200787 -109221651 230674393235 -1919209135381395 63379954960524853651 |
| Alt | CentralOT(2 n + 1, n) | A218449 | 1 -7 155 -11811 3309747 -3548836819 14877590196755 -246614610741341843 16256896431763117598611 |
| Alt | 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 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 0 92 0 -9124 0 3774172 0 -6459170980 0 45480123143132 0 -1310657322035590052 0 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 8 -44 332 -3412 48188 -940564 25545052 -969582644 51635485244 -3867743513812 408350633776412 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -1 4 14 -67 -651 4438 110236 -1159249 -70413245 1199994376 172963095018 -4942804152223 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -2 4 21 -67 -868 4438 137795 -1159249 -84495894 1199994376 201790277521 -4942804152223 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 1 12 6 -335 -1137 31066 328436 -10433241 -292256139 13199938136 912947335314 -64256453978899 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 -7 7 217 -217 -27559 27559 14082649 -14082649 -28827182503 28827182503 236123451882073 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A182176 | 1 -3 11 -51 307 -2451 26387 -387987 7866259 -221472147 8703733139 -479243212179 37070813107603 |
| Alt | DiagRow1T(n + 1, n) | A000225 | 1 -3 7 -15 31 -63 127 -255 511 -1023 2047 -4095 8191 -16383 32767 -65535 131071 -262143 524287 |
| Alt | DiagRow2T(n + 2, n) | A006095 | 1 -7 35 -155 651 -2667 10795 -43435 174251 -698027 2794155 -11180715 44731051 -178940587 715795115 |
| Alt | DiagRow3T(n + 3, n) | A006096 | 1 -15 155 -1395 11811 -97155 788035 -6347715 50955971 -408345795 3269560515 -26167664835 |
| Alt | DiagCol1T(n + 1, 1) | A000225 | -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Alt | DiagCol2T(n + 2, 2) | A006095 | 1 7 35 155 651 2667 10795 43435 174251 698027 2794155 11180715 44731051 178940587 715795115 |
| Alt | DiagCol3T(n + 3, 3) | A006096 | -1 -15 -155 -1395 -11811 -97155 -788035 -6347715 -50955971 -408345795 -3269560515 -26167664835 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 0 -1 -2 1 1 7 7 1 -3 1 1 0 7 16 5 -4 1 1 -217 -217 -53 21 11 -5 1 1 0 -217 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Alt | PolyRow2∑ k=0..2 T(2, 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 7 16 21 16 -5 -48 -119 -224 -369 -560 -803 -1104 -1469 -1904 -2415 -3008 -3689 -4464 -5339 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 -1 7 7 -217 -217 27559 27559 -14082649 -14082649 28827182503 28827182503 -236123451882073 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 1 16 -53 -614 6157 103732 -2553281 -74248418 4062676609 219743041624 -25388383139117 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 16 -203 596 122203 -6269556 -98358071 58362339448 -3712118530129 -1822976642783240 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A135950 | 1 -1 1 2 -3 1 -8 14 -7 1 64 -120 70 -15 1 -1024 1984 -1240 310 -31 1 32768 -64512 41664 -11160 1302 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A158474 | 1 1 -1 1 -3 2 1 -7 14 -8 1 -15 70 -120 64 1 -31 310 -1240 1984 -1024 1 -63 1302 -11160 41664 -64512 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A022166 | 1 1 1 1 3 1 1 7 7 1 1 15 35 15 1 1 31 155 155 31 1 1 63 651 1395 651 63 1 1 127 2667 11811 11811 |
| Inv | Accsee docs | missing | 1 -1 0 2 -1 0 -8 6 -1 0 64 -56 14 -1 0 -1024 960 -280 30 -1 0 32768 -31744 9920 -1240 62 -1 0 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -2 0 1 -6 8 0 1 -14 56 -64 0 1 -30 280 -960 1024 0 1 -62 1240 -9920 31744 -32768 0 1 -126 |
| Inv | AntiDiagsee docs | missing | 1 -1 2 1 -8 -3 64 14 1 -1024 -120 -7 32768 1984 70 1 -2097152 -64512 -1240 -15 268435456 4161536 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 2 -6 3 -8 28 -21 4 64 -240 210 -60 5 -1024 3968 -3720 1240 -155 6 32768 -129024 124992 |
| Inv | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A028362 | 1 -1 3 -15 135 -2295 75735 -4922775 635037975 -163204759575 83724041661975 -85817142703524375 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A028362 | 0 1 -3 15 -135 2295 -75735 4922775 -635037975 163204759575 -83724041661975 85817142703524375 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A028361 | 1 -2 6 -30 270 -4590 151470 -9845550 1270075950 -326409519150 167448083323950 -171634285407048750 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A028361 | 1 2 6 30 270 4590 151470 9845550 1270075950 326409519150 167448083323950 171634285407048750 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 3 -11 79 -1151 34823 -2162919 272638967 -69256992695 35321897094615 -36099188233043287 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A005329 | 1 -1 1 -3 21 -315 9765 -615195 78129765 -19923090075 10180699028325 -10414855105976475 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A005329 | 1 1 -1 3 -21 315 -9765 615195 -78129765 19923090075 -10180699028325 10414855105976475 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 56 6720 158720 319979520 173386235904 808475248558080 1137220409842728960 |
| 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) | | A127850 | 1 1 3 14 120 1984 64512 4161536 534773760 137170518016 70300024700928 72022409665839104 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -3 14 70 -1240 -11160 755904 12850368 -3389180928 -111842970624 116288284884992 |
| Inv | CentralET(2 n, n) | A135951 | 1 -3 70 -11160 12850368 -111842970624 7558738517524480 -4024873276683363287040 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 14 -1240 755904 -3389180928 116288284884992 -31200568036305141760 66200105490614595677585408 |
| Inv | ColLeftT(n, 0) | A006125 | 1 -1 2 -8 64 -1024 32768 -2097152 268435456 -68719476736 35184372088832 -36028797018963968 |
| 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 0 -3 14 -55 -558 66609 -7056882 1180047537 -345215150910 181970174430825 -172524467631059058 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 9 72 1025 26600 1287909 118455696 20965995297 7205821917296 4839261283120341 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A005329 | 0 1 -1 3 -21 315 -9765 615195 -78129765 19923090075 -10180699028325 10414855105976475 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A005329 | 1 1 -1 3 -21 315 -9765 615195 -78129765 19923090075 -10180699028325 10414855105976475 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 1 -5 41 -657 20997 -1342341 171707697 -43941722265 22494066257565 -23031791179545645 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A005329 | 1 -1 3 -21 315 -9765 615195 -78129765 19923090075 -10180699028325 10414855105976475 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A028362 | 1 3 15 135 2295 75735 4922775 635037975 163204759575 83724041661975 85817142703524375 |
| Inv | DiagRow1T(n + 1, n) | A000225 | -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Inv | DiagRow2T(n + 2, n) | A203241 | 2 14 70 310 1302 5334 21590 86870 348502 1396054 5588310 22361430 89462102 357881174 1431590230 |
| Inv | DiagRow3T(n + 3, n) | missing | -8 -120 -1240 -11160 -94488 -777240 -6304280 -50781720 -407647768 -3266766360 -26156484120 |
| Inv | DiagCol1T(n + 1, 1) | A127850 | 1 -3 14 -120 1984 -64512 4161536 -534773760 137170518016 -70300024700928 72022409665839104 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -7 70 -1240 41664 -2731008 353730560 -91089797120 46775146643456 -47968050187599872 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -15 310 -11160 755904 -99486720 25822330880 -13312123207680 13678389311307776 |
| Inv | Polysee docs | missing | 1 -1 1 2 0 1 -8 0 1 1 64 0 0 2 1 -1024 0 0 2 3 1 32768 0 0 -2 6 4 1 -2097152 0 0 10 0 12 5 1 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A002378 | 2 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 | -8 0 0 -2 0 12 40 90 168 280 432 630 880 1188 1560 2002 2520 3120 3808 4590 5472 6460 7560 8778 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^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 | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 2 -2 10 -130 3770 -229970 28746250 -7272801250 3701855836250 -3779594808811250 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 -2 0 396 -20800 1154250 0 -72877004200 89743347505152 -153012210826088250 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A158474 | 1 1 -1 1 -3 2 1 -7 14 -8 1 -15 70 -120 64 1 -31 310 -1240 1984 -1024 1 -63 1302 -11160 41664 -64512 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A135950 | 1 -1 1 2 -3 1 -8 14 -7 1 64 -120 70 -15 1 -1024 1984 -1240 310 -31 1 32768 -64512 41664 -11160 1302 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A022166 | 1 1 1 1 3 1 1 7 7 1 1 15 35 15 1 1 31 155 155 31 1 1 63 651 1395 651 63 1 1 127 2667 11811 11811 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -2 0 1 -6 8 0 1 -14 56 -64 0 1 -30 280 -960 1024 0 1 -62 1240 -9920 31744 -32768 0 1 -126 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 2 -1 0 -8 6 -1 0 64 -56 14 -1 0 -1024 960 -280 30 -1 0 32768 -31744 9920 -1240 62 -1 0 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -3 1 -7 2 1 -15 14 1 -31 70 -8 1 -63 310 -120 1 -127 1302 -1240 64 1 -255 5334 -11160 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -6 6 1 -14 42 -32 1 -30 210 -480 320 1 -62 930 -4960 9920 -6144 1 -126 3906 -44640 208320 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A028362 | 1 1 3 15 135 2295 75735 4922775 635037975 163204759575 83724041661975 85817142703524375 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A028362 | 0 -1 -3 -15 -135 -2295 -75735 -4922775 -635037975 -163204759575 -83724041661975 -85817142703524375 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A028361 | 1 2 6 30 270 4590 151470 9845550 1270075950 326409519150 167448083323950 171634285407048750 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A028361 | 1 2 6 30 270 4590 151470 9845550 1270075950 326409519150 167448083323950 171634285407048750 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -2 -4 0 32 128 0 -4096 -32768 0 4194304 67108864 0 -34359738368 -1099511627776 0 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A005329 | 1 1 -1 3 -21 315 -9765 615195 -78129765 19923090075 -10180699028325 10414855105976475 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A005329 | 1 -1 1 -3 21 -315 9765 -615195 78129765 -19923090075 10180699028325 -10414855105976475 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 56 6720 158720 319979520 173386235904 808475248558080 1137220409842728960 |
| 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) | | A127850 | 1 1 3 14 120 1984 64512 4161536 534773760 137170518016 70300024700928 72022409665839104 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -3 -7 70 310 -11160 -94488 12850368 211823808 -111842970624 -3634008902656 7558738517524480 |
| Inv:Rev | CentralET(2 n, n) | A135951 | 1 -3 70 -11160 12850368 -111842970624 7558738517524480 -4024873276683363287040 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -7 310 -94488 211823808 -3634008902656 487508875567267840 -517188324145426528731136 |
| 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) | A006125 | 1 -1 2 -8 64 -1024 32768 -2097152 268435456 -68719476736 35184372088832 -36028797018963968 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 14 -55 -558 66609 -7056882 1180047537 -345215150910 181970174430825 -172524467631059058 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 9 -72 1025 -26600 1287909 -118455696 20965995297 -7205821917296 4839261283120341 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A005329 | 0 -1 1 -3 21 -315 9765 -615195 78129765 -19923090075 10180699028325 -10414855105976475 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A005329 | 1 -1 1 -3 21 -315 9765 -615195 78129765 -19923090075 10180699028325 -10414855105976475 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 5 -23 209 -3807 138177 -9955071 1421783937 -402557343615 226108046824065 -252158603511028095 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^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 | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A139486 | 1 -3 12 -72 720 -12960 440640 -29082240 3780691200 -975418329600 501365021414400 |
| Inv:Rev | DiagRow1T(n + 1, n) | A127850 | 1 -3 14 -120 1984 -64512 4161536 -534773760 137170518016 -70300024700928 72022409665839104 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -7 70 -1240 41664 -2731008 353730560 -91089797120 46775146643456 -47968050187599872 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -15 310 -11160 755904 -99486720 25822330880 -13312123207680 13678389311307776 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000225 | -1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A203241 | 2 14 70 310 1302 5334 21590 86870 348502 1396054 5588310 22361430 89462102 357881174 1431590230 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -8 -120 -1240 -11160 -94488 -777240 -6304280 -50781720 -407647768 -3266766360 -26156484120 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 3 -2 1 1 0 -21 10 -3 1 1 0 315 -110 21 -4 1 1 0 -9765 2530 -315 36 -5 1 1 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A014105 | 1 0 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 528 595 666 741 820 903 990 1081 1176 1275 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 -21 -110 -315 -684 -1265 -2106 -3255 -4760 -6669 -9030 -11891 -15300 -19305 -23954 -29295 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A005329 | 1 -1 3 -21 315 -9765 615195 -78129765 19923090075 -10180699028325 10414855105976475 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 10 -110 2530 -118910 11296450 -2157621950 826369206850 -633825181653950 972921653838813250 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 3 -110 9765 -2107404 1078810975 -1281611575530 3471618368658825 -21140747635478471000 |
| << | 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.