OEIS Similars: A132062, A001497, A001498, A122850
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A132062 | 1 0 1 0 1 1 0 3 3 1 0 15 15 6 1 0 105 105 45 10 1 0 945 945 420 105 15 1 0 10395 10395 4725 1260 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A104548 | 1 1 0 1 1 0 1 3 3 0 1 6 15 15 0 1 10 45 105 105 0 1 15 105 420 945 945 0 1 21 210 1260 4725 10395 |
| Std | Accsee docs | missing | 1 0 1 0 1 2 0 3 6 7 0 15 30 36 37 0 105 210 255 265 266 0 945 1890 2310 2415 2430 2431 0 10395 |
| Std | AccRevsee docs | missing | 1 1 1 1 2 2 1 4 7 7 1 7 22 37 37 1 11 56 161 266 266 1 16 121 541 1486 2431 2431 1 22 232 1492 6217 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 1 0 3 1 0 15 3 0 105 15 1 0 945 105 6 0 10395 945 45 1 0 135135 10395 420 10 0 2027025 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 2 3 0 6 9 4 0 30 45 24 5 0 210 315 180 50 6 0 1890 2835 1680 525 90 7 0 20790 31185 18900 |
| Std | RowSum∑ k=0..n T(n, k) | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A036244 | 1 0 1 3 16 115 1051 11676 152839 2304261 39325276 749484505 15778499881 363654981768 9107153044081 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A025164 | 0 1 1 4 21 151 1380 15331 200683 3025576 51635475 984099601 20717727096 477491822809 11958013297321 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A278990 | 1 -1 0 -1 -5 -36 -329 -3655 -47844 -721315 -12310199 -234615096 -4939227215 -113836841041 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 1 4 18 121 1056 11386 145960 2166991 36550095 690151981 14420529291 330298370704 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 3 16 118 1101 12421 164473 2501661 42992218 823976596 17426801811 403192080853 10130257881901 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 5 19 104 761 7027 78590 1033559 15635989 267552416 5109791567 107755096825 2486944186754 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 30 630 3780 207900 8108100 56756700 1929727800 329983453800 549972423000 139143023019000 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Std | RowMaxMax k=0..n | T(n, k) | | A001147 | 1 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 1 3 15 105 420 4725 17325 270270 945945 18918900 64324260 1571349780 5237832600 151242416325 |
| Std | CentralET(2 n, n) | A376872 | 1 1 15 420 17325 945945 64324260 5237832600 496939367925 53835098191875 6557114959770375 |
| Std | CentralOT(2 n + 1, n) | missing | 0 3 105 4725 270270 18918900 1571349780 151242416325 16564645597500 2034966711652875 |
| 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) | missing | 1 1 3 19 175 2076 29911 505093 9757539 211883500 5102919316 134868653976 3878398876573 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -1 1 7 -124 1591 -19991 256691 -3335228 41759236 -430787224 595905949 182463444151 |
| Std | TransNat0∑ k=0..n T(n, k) k | A107103 | 0 1 3 12 67 495 4596 51583 680037 10306152 176591665 3376207461 71258869848 1645797382177 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 5 19 104 761 7027 78590 1033559 15635989 267552416 5109791567 107755096825 2486944186754 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 5 24 145 1115 10596 120715 1607999 24555060 423178255 8127485861 172170591000 3988490245129 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001517 | 1 1 3 19 193 2721 49171 1084483 28245729 848456353 28875761731 1098127402131 46150226651233 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A002119 | 1 1 -1 7 -71 1001 -18089 398959 -10391023 312129649 -10622799089 403978495031 -16977719590391 |
| 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) | A050534 | 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
| Std | DiagRow3T(n + 3, n) | A240440 | 0 15 105 420 1260 3150 6930 13860 25740 45045 75075 120120 185640 278460 406980 581400 813960 |
| Std | DiagCol1T(n + 1, 1) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Std | DiagCol2T(n + 2, 2) | A001147 | 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Std | DiagCol3T(n + 3, 3) | A001879 | 1 6 45 420 4725 62370 945945 16216200 310134825 6547290750 151242416325 3794809718700 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 7 6 3 1 0 37 26 12 4 1 0 266 154 63 20 5 1 0 2431 1182 423 124 30 6 1 0 27007 |
| 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 | A068601 | 0 7 26 63 124 215 342 511 728 999 1330 1727 2196 2743 3374 4095 4912 5831 6858 7999 9260 10647 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A107104 | 1 2 6 26 154 1182 11254 128522 1715802 26251118 453132214 8714516538 184817376154 4285657717694 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A369746 | 1 3 12 63 423 3528 35559 422901 5817744 91072269 1600588269 31230827532 670252672593 15696888917427 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 6 63 940 18150 429786 12051697 390433464 14347598445 589633486750 26794524373716 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A132062 | 1 0 -1 0 -1 1 0 -3 3 -1 0 -15 15 -6 1 0 -105 105 -45 10 -1 0 -945 945 -420 105 -15 1 0 -10395 10395 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A104548 | 1 -1 0 1 -1 0 -1 3 -3 0 1 -6 15 -15 0 -1 10 -45 105 -105 0 1 -15 105 -420 945 -945 0 -1 21 -210 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 0 -3 1 0 0 -33 6 1 0 0 90 -15 -10 1 0 0 2610 -435 -255 15 1 0 0 -18900 3150 1995 -105 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -3 0 0 1 6 -33 0 0 1 -10 -15 90 0 0 1 15 -255 -435 2610 0 0 1 -21 -105 1995 3150 |
| Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 -3 0 -1 0 -15 0 -6 -5 0 -105 0 -45 -35 -36 0 -945 0 -420 -315 -330 -329 0 -10395 0 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 2 -1 -1 1 -5 10 -5 -5 -1 9 -36 69 -36 -36 1 -14 91 -329 616 -329 -329 -1 20 -190 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -1 0 -3 1 0 -15 3 0 -105 15 -1 0 -945 105 -6 0 -10395 945 -45 1 0 -135135 10395 -420 10 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -2 3 0 -6 9 -4 0 -30 45 -24 5 0 -210 315 -180 50 -6 0 -1890 2835 -1680 525 -90 7 0 -20790 |
| Alt | RowSum∑ k=0..n T(n, k) | A278990 | 1 -1 0 -1 -5 -36 -329 -3655 -47844 -721315 -12310199 -234615096 -4939227215 -113836841041 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A036244 | 1 0 1 3 16 115 1051 11676 152839 2304261 39325276 749484505 15778499881 363654981768 9107153044081 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A025164 | 0 -1 -1 -4 -21 -151 -1380 -15331 -200683 -3025576 -51635475 -984099601 -20717727096 -477491822809 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -1 -2 -12 -91 -846 -9494 -125150 -1896511 -32493525 -621198479 -13110530559 -302790289348 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 -4 -26 -221 -2339 -29569 -434251 -7260994 -136133504 -2827691351 -64444568891 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A003436 | 1 -2 1 -1 -4 -31 -293 -3326 -44189 -673471 -11588884 -222304897 -4704612119 -108897613826 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 30 630 3780 207900 8108100 56756700 1929727800 329983453800 549972423000 139143023019000 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A001147 | 1 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -1 -3 15 105 -420 -4725 17325 270270 -945945 -18918900 64324260 1571349780 -5237832600 |
| Alt | CentralET(2 n, n) | A376872 | 1 -1 15 -420 17325 -945945 64324260 -5237832600 496939367925 -53835098191875 6557114959770375 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -3 105 -4725 270270 -18918900 1571349780 -151242416325 16564645597500 -2034966711652875 |
| 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) | missing | 1 -1 -1 -1 7 124 1591 19991 256691 3335228 41759236 430787224 595905949 -182463444151 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -19 175 -2076 29911 -505093 9757539 -211883500 5102919316 -134868653976 3878398876573 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A278990 | 0 -1 1 0 1 5 36 329 3655 47844 721315 12310199 234615096 4939227215 113836841041 2850860253240 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A003436 | 1 -2 1 -1 -4 -31 -293 -3326 -44189 -673471 -11588884 -222304897 -4704612119 -108897613826 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 3 0 7 45 396 4277 54825 813348 13704985 258514179 5396147208 123480680375 3073594708107 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A002119 | 1 -1 -1 -7 -71 -1001 -18089 -398959 -10391023 -312129649 -10622799089 -403978495031 -16977719590391 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001517 | 1 -1 3 -19 193 -2721 49171 -1084483 28245729 -848456353 28875761731 -1098127402131 46150226651233 |
| 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) | A050534 | 0 -3 15 -45 105 -210 378 -630 990 -1485 2145 -3003 4095 -5460 7140 -9180 11628 -14535 17955 -21945 |
| Alt | DiagRow3T(n + 3, n) | A240440 | 0 -15 105 -420 1260 -3150 6930 -13860 25740 -45045 75075 -120120 185640 -278460 406980 -581400 |
| Alt | DiagCol1T(n + 1, 1) | A001147 | -1 -1 -3 -15 -105 -945 -10395 -135135 -2027025 -34459425 -654729075 -13749310575 -316234143225 |
| Alt | DiagCol2T(n + 2, 2) | A001147 | 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Alt | DiagCol3T(n + 3, 3) | A001879 | -1 -6 -45 -420 -4725 -62370 -945945 -16216200 -310134825 -6547290750 -151242416325 -3794809718700 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 0 -2 1 0 -1 2 -3 1 0 -5 -2 6 -4 1 0 -36 -2 -9 12 -5 1 0 -329 -22 9 -28 20 -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 | 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 | A001093 | 0 -1 -2 -9 -28 -65 -126 -217 -344 -513 -730 -1001 -1332 -1729 -2198 -2745 -3376 -4097 -4914 -5833 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 2 -2 -2 -22 -206 -2354 -31426 -480806 -8299406 -159611938 -3385048322 -78494559158 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 6 -9 9 -18 -81 -1053 -14418 -225747 -3967461 -77413482 -1661390271 -38908697571 -987669951714 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 2 -9 52 -400 3726 -41209 525512 -7601283 122898250 -2196729106 43010133948 -915436196701 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A104548 | 1 1 0 1 1 0 1 3 3 0 1 6 15 15 0 1 10 45 105 105 0 1 15 105 420 945 945 0 1 21 210 1260 4725 10395 |
| Rev | Accsee docs | missing | 1 1 1 1 2 2 1 4 7 7 1 7 22 37 37 1 11 56 161 266 266 1 16 121 541 1486 2431 2431 1 22 232 1492 6217 |
| Rev | AccRevsee docs | missing | 1 0 1 0 1 2 0 3 6 7 0 15 30 36 37 0 105 210 255 265 266 0 945 1890 2310 2415 2430 2431 0 10395 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 3 0 1 6 3 1 10 15 0 1 15 45 15 1 21 105 105 0 1 28 210 420 105 1 36 378 1260 945 0 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 6 9 0 1 12 45 60 0 1 20 135 420 525 0 1 30 315 1680 4725 5670 0 1 42 630 5040 23625 |
| Rev | RowSum∑ k=0..n T(n, k) | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 4 16 151 1051 15331 152839 3025576 39325276 984099601 15778499881 477491822809 9107153044081 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 1 3 21 115 1380 11676 200683 2304261 51635475 749484505 20717727096 363654981768 11958013297321 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A278990 | 1 1 0 1 -5 36 -329 3655 -47844 721315 -12310199 234615096 -4939227215 113836841041 -2850860253240 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A001515 | 1 1 2 7 37 266 2431 27007 353522 5329837 90960751 1733584106 36496226977 841146804577 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A000085 | 1 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 5 19 104 761 7027 78590 1033559 15635989 267552416 5109791567 107755096825 2486944186754 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 3 16 118 1101 12421 164473 2501661 42992218 823976596 17426801811 403192080853 10130257881901 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 30 630 3780 207900 8108100 56756700 1929727800 329983453800 549972423000 139143023019000 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A001147 | 1 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 1 3 15 45 420 1260 17325 51975 945945 2837835 64324260 192972780 5237832600 15713497800 |
| Rev | CentralET(2 n, n) | A376872 | 1 1 15 420 17325 945945 64324260 5237832600 496939367925 53835098191875 6557114959770375 |
| Rev | CentralOT(2 n + 1, n) | A245066 | 1 3 45 1260 51975 2837835 192972780 15713497800 1490818103775 161505294575625 19671344879311125 |
| 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) | missing | 1 1 3 19 175 2076 29911 505093 9757539 211883500 5102919316 134868653976 3878398876573 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -1 -1 7 124 1591 19991 256691 3335228 41759236 430787224 595905949 -182463444151 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A001514 | 0 0 1 9 81 835 9990 137466 2148139 37662381 733015845 15693217705 366695853876 9289111077324 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 3 16 118 1101 12421 164473 2501661 42992218 823976596 17426801811 403192080853 10130257881901 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 1 15 201 2815 42960 721896 13352815 270761121 5987420055 143614598545 3717414399336 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A107104 | 1 2 6 26 154 1182 11254 128522 1715802 26251118 453132214 8714516538 184817376154 4285657717694 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 2 -2 -2 -22 -206 -2354 -31426 -480806 -8299406 -159611938 -3385048322 -78494559158 |
| Rev | DiagRow1T(n + 1, n) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Rev | DiagRow2T(n + 2, n) | A001147 | 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Rev | DiagRow3T(n + 3, n) | A001879 | 1 6 45 420 4725 62370 945945 16216200 310134825 6547290750 151242416325 3794809718700 |
| 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) | A050534 | 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
| Rev | DiagCol3T(n + 3, 3) | A240440 | 0 15 105 420 1260 3150 6930 13860 25740 45045 75075 120120 185640 278460 406980 581400 813960 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 7 3 1 1 1 37 19 4 1 1 1 266 193 37 5 1 1 1 2431 2721 559 61 6 1 1 1 27007 |
| 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 | A003215 | 1 7 19 37 61 91 127 169 217 271 331 397 469 547 631 721 817 919 1027 1141 1261 1387 1519 1657 1801 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A001517 | 1 1 3 19 193 2721 49171 1084483 28245729 848456353 28875761731 1098127402131 46150226651233 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A001518 | 1 1 4 37 559 11776 318511 10522639 410701432 18492087079 943507142461 53798399207356 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 3 37 1225 79926 8667631 1409457463 320939805537 97470996613525 38072355184809451 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A104548 | 1 1 0 1 1 0 1 3 3 0 1 6 15 15 0 1 10 45 105 105 0 1 15 105 420 945 945 0 1 21 210 1260 4725 10395 |
| Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 0 -3 -2 0 0 3 -3 -2 0 0 0 15 5 6 0 0 0 -15 30 15 16 0 0 0 0 -105 0 -21 -20 0 0 0 0 |
| Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 -2 -2 -2 1 -5 -2 -2 -2 1 -9 6 6 6 6 1 -14 31 16 16 16 16 1 -20 85 -20 -20 -20 -20 -20 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 0 1 0 0 -3 0 0 3 1 0 0 0 -6 0 0 0 15 1 0 0 0 -15 -10 0 0 0 0 45 1 0 0 0 0 -105 -15 0 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 0 -9 4 0 0 9 -24 5 0 0 0 60 -50 6 0 0 0 -60 225 -90 7 0 0 0 0 -525 630 -147 8 0 0 0 |
| Inv | RowSum∑ k=0..n T(n, k) | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A085386 | 1 0 1 -3 4 -10 46 -126 316 -1296 5356 -17380 63856 -296088 1264264 -4940040 22302736 -110455936 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -1 1 -6 16 -30 106 -448 1324 -4140 18316 -76296 272416 -1126216 5409496 -23904000 101343376 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A000085 | 1 -1 2 -4 10 -26 76 -232 764 -2620 9496 -35696 140152 -568504 2390480 -10349536 46206736 -211799312 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -1 1 -3 4 -6 16 -25 46 -120 211 -441 1156 -2233 5104 -13581 28351 -69345 188101 -419320 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 -5 -2 26 46 -146 -580 748 7156 -604 -92696 -96680 1270088 2955016 -18167024 -72958576 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 1 -5 -10 16 82 -34 -740 -440 7436 12772 -81464 -258400 938680 5025736 -10655728 -100180064 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Inv | ColMiddleT(n, n // 2) | A123023 | 1 0 -1 0 3 0 -15 0 105 0 -945 0 10395 0 -135135 0 2027025 0 -34459425 0 654729075 0 -13749310575 0 |
| Inv | CentralET(2 n, n) | A001147 | 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
| 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 -8 -5 101 286 -1616 -10513 26515 404011 -174844 -17016416 -26519648 782613560 2994914896 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 3 10 43 201 1066 6028 36975 238843 1637191 11718246 87877648 683880640 5530539288 46195085056 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 1 -3 -8 10 66 -14 -608 -468 6220 11836 -69024 -234728 800632 4556280 -9054464 -91067504 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 1 -5 -10 16 82 -34 -740 -440 7436 12772 -81464 -258400 938680 5025736 -10655728 -100180064 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 -3 -26 0 246 238 -2568 -5436 28900 105996 -337512 -2055248 3795624 41212200 -32229824 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A293604 | 1 1 -1 -5 1 41 31 -461 -895 6481 22591 -107029 -604031 1964665 17669471 -37341149 -567425279 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A047974 | 1 1 3 7 25 81 331 1303 5937 26785 133651 669351 3609673 19674097 113525595 664400311 4070168161 |
| 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) | A050534 | 0 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
| Inv | DiagRow3T(n + 3, n) | A240440 | 0 0 0 -15 -105 -420 -1260 -3150 -6930 -13860 -25740 -45045 -75075 -120120 -185640 -278460 -406980 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | DiagCol3T(n + 3, 3) | missing | 1 -6 15 -15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 -2 2 3 1 0 -2 -4 6 4 1 0 6 -20 0 12 5 1 0 16 -8 -54 16 20 6 1 0 -20 184 -162 |
| 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 -2 -4 0 16 50 108 196 320 486 700 968 1296 1690 2156 2700 3328 4046 4860 5776 6800 7938 9196 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A062267 | 1 2 2 -4 -20 -8 184 464 -1648 -10720 8224 230848 280768 -4978816 -17257600 104891648 727511296 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 6 0 -54 -162 324 3888 4860 -78732 -367416 1259712 15903864 2361960 -613164816 -1938696768 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 2 0 -80 -1250 -14904 -134456 -225280 31886460 1130500000 26814347296 454786265088 2381933705320 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A132062 | 1 0 1 0 1 1 0 3 3 1 0 15 15 6 1 0 105 105 45 10 1 0 945 945 420 105 15 1 0 10395 10395 4725 1260 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 -2 -2 -2 1 -5 -2 -2 -2 1 -9 6 6 6 6 1 -14 31 16 16 16 16 1 -20 85 -20 -20 -20 -20 -20 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 0 -3 -2 0 0 3 -3 -2 0 0 0 15 5 6 0 0 0 -15 30 15 16 0 0 0 0 -105 0 -21 -20 0 0 0 0 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -3 0 1 -6 0 1 -10 3 0 1 -15 15 0 1 -21 45 0 0 1 -28 105 -15 0 1 -36 210 -105 0 0 1 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -6 0 0 1 -12 9 0 0 1 -20 45 0 0 0 1 -30 135 -60 0 0 0 1 -42 315 -420 0 0 0 0 1 -56 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A001464 | 1 1 0 -2 -2 6 16 -20 -132 28 1216 936 -12440 -23672 138048 469456 -1601264 -9112560 18108928 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A000704 | 1 1 1 1 4 16 46 106 316 1324 5356 18316 63856 272416 1264264 5409496 22302736 101343376 507711376 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A001465 | 0 0 -1 -3 -6 -10 -30 -126 -448 -1296 -4140 -17380 -76296 -296088 -1126216 -4940040 -23904000 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A000085 | 1 1 2 4 10 26 76 232 764 2620 9496 35696 140152 568504 2390480 10349536 46206736 211799312 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 -2 -5 -6 1 25 63 70 -86 -579 -1280 -797 4575 18739 31696 -14310 -248267 -717170 -687441 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 1 -5 -10 16 82 -34 -740 -440 7436 12772 -81464 -258400 938680 5025736 -10655728 -100180064 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 -5 -2 26 46 -146 -580 748 7156 -604 -92696 -96680 1270088 2955016 -18167024 -72958576 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 3 6 30 45 105 420 3780 9450 103950 623700 540540 945945 14189175 113513400 1929727800 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A069834 | 1 1 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17 153 171 95 105 231 253 69 75 325 351 189 203 435 465 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 3 6 15 45 105 420 1260 4725 17325 62370 270270 945945 4729725 18918900 91891800 413513100 |
| Inv:Rev | ColMiddleT(n, n // 2) | A133221 | 1 1 -1 -3 3 15 -15 -105 105 945 -945 -10395 10395 135135 -135135 -2027025 2027025 34459425 |
| Inv:Rev | CentralET(2 n, n) | A001147 | 1 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225 |
| Inv:Rev | CentralOT(2 n + 1, n) | A001147 | 1 -3 15 -105 945 -10395 135135 -2027025 34459425 -654729075 13749310575 -316234143225 7905853580625 |
| 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 -8 -5 101 286 -1616 -10513 26515 404011 -174844 -17016416 -26519648 782613560 2994914896 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -10 43 -201 1066 -6028 36975 -238843 1637191 -11718246 87877648 -683880640 5530539288 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -1 -3 0 20 30 -126 -448 720 5940 -1540 -80256 -73008 1132040 2485560 -16565760 -63846016 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 -5 -2 26 46 -146 -580 748 7156 -604 -92696 -96680 1270088 2955016 -18167024 -72958576 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 -3 6 50 30 -546 -1288 5256 26100 -41140 -472296 47112 8435336 10151400 -152410560 -401882176 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A062267 | 1 2 2 -4 -20 -8 184 464 -1648 -10720 8224 230848 280768 -4978816 -17257600 104891648 727511296 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000898 | 1 -2 6 -20 76 -312 1384 -6512 32400 -168992 921184 -5222208 30710464 -186753920 1171979904 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | DiagRow3T(n + 3, n) | missing | 1 -6 15 -15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | 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) | A050534 | 0 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460 7140 9180 11628 14535 17955 21945 26565 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A240440 | 0 0 0 -15 -105 -420 -1260 -3150 -6930 -13860 -25740 -45045 -75075 -120120 -185640 -278460 -406980 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 -2 -1 1 1 1 -2 -5 -2 1 1 1 6 1 -8 -3 1 1 1 16 41 10 -11 -4 1 1 1 -20 31 106 |
| 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 | A016789 | 1 -2 -5 -8 -11 -14 -17 -20 -23 -26 -29 -32 -35 -38 -41 -44 -47 -50 -53 -56 -59 -62 -65 -68 -71 -74 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A293604 | 1 1 -1 -5 1 41 31 -461 -895 6481 22591 -107029 -604031 1964665 17669471 -37341149 -567425279 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A362278 | 1 1 -2 -8 10 106 -44 -1952 -1028 45820 73576 -1301024 -3729032 43107832 188540080 -1621988864 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A362276 | 1 1 -1 -8 25 326 -1709 -31016 228257 5311900 -50337449 -1429574464 16573668409 555724876552 |
| << | 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.