OEIS Similars: A165675, A093905, A105954, A165674
↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
---|---|---|---|
Std | TriangleT(n, k), 0 ≤ k ≤ n | A165675 | 1 1 1 2 3 1 6 11 5 1 24 50 26 7 1 120 274 154 47 9 1 720 1764 1044 342 74 11 1 5040 13068 8028 2754 |
Std | RevT(n, n - k), 0 ≤ k ≤ n | A105954 | 1 1 1 1 3 2 1 5 11 6 1 7 26 50 24 1 9 47 154 274 120 1 11 74 342 1044 1764 720 1 13 107 638 2754 |
Std | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -3 1 0 4 -5 1 0 0 9 -7 1 0 0 0 16 -9 1 0 0 0 0 25 -11 1 0 0 0 0 0 36 -13 1 0 0 0 0 0 0 49 |
Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 1 1 -5 4 0 1 -7 9 0 0 1 -9 16 0 0 0 1 -11 25 0 0 0 0 1 -13 36 0 0 0 0 0 1 -15 49 0 0 0 |
Std | Accsee docs | missing | 1 1 2 2 5 6 6 17 22 23 24 74 100 107 108 120 394 548 595 604 605 720 2484 3528 3870 3944 3955 3956 |
Std | AccRevsee docs | missing | 1 1 2 1 4 6 1 6 17 23 1 8 34 84 108 1 10 57 211 485 605 1 12 86 428 1472 3236 3956 1 14 121 759 |
Std | AntiDiagsee docs | missing | 1 1 2 1 6 3 24 11 1 120 50 5 720 274 26 1 5040 1764 154 7 40320 13068 1044 47 1 362880 109584 8028 |
Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 6 3 6 22 15 4 24 100 78 28 5 120 548 462 188 45 6 720 3528 3132 1368 370 66 7 5040 26136 |
Std | RowSum∑ k=0..n T(n, k) | A093345 | 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 |
Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 11 51 283 1839 13719 115675 1088459 11311047 128686087 1591143315 21247786347 304787011135 |
Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 3 12 57 322 2117 15930 135217 1279170 13351653 152467714 1891207409 25324834410 364156476949 |
Std | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 0 0 -1 -6 -39 -278 -2211 -19542 -190711 -2040606 -23781627 -300064094 -4077048063 -59369465814 |
Std | AbsSum∑ k=0..n | T(n, k) | | A093345 | 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 |
Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 3 9 36 175 1021 6965 54480 480843 4727469 51234337 606792460 7796744735 108019499901 |
Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 13 68 413 2866 22457 196634 1906165 20290322 235457201 2959959922 40086920909 582025267370 |
Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 11 47 235 1369 9191 70207 602755 5753597 60495199 695039491 8665989227 116564043985 |
Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 330 54600 178489080 7911786960 839338855795440 11191805812769662080 |
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) | | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
Std | ColMiddleT(n, n // 2) | missing | 1 1 3 11 26 154 342 2754 5944 60216 127860 1557660 3272688 46536624 97053936 1576890000 3270729600 |
Std | CentralET(2 n, n) | missing | 1 3 26 342 5944 127860 3272688 97053936 3270729600 123418922400 5154170774400 235977273544320 |
Std | CentralOT(2 n + 1, n) | missing | 1 11 154 2754 60216 1557660 46536624 1576890000 59753750400 2503748556000 114942011990400 |
Std | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
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 9 55 409 3546 34981 386163 4711281 62903242 911810321 14254347735 238977876457 4275994190482 |
Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -3 13 -47 136 1 -5935 88481 -1060568 11963541 -131894883 1423461073 -14655258656 132538911961 |
Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 5 24 127 764 5235 40558 351863 3385968 35832499 413885690 5183638503 69991423228 1013733520163 |
Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 11 47 235 1369 9191 70207 602755 5753597 60495199 695039491 8665989227 116564043985 |
Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 7 40 233 1482 10513 83366 735417 7166746 76599497 891914958 11245505041 152701872242 |
Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 15 103 903 9663 122287 1787991 29671479 551104591 11328415263 255351604647 6263220826471 |
Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 3 -13 75 -517 3875 -26301 29531 5729003 -227270157 7253745395 -223673532181 7005519261531 |
Std | DiagRow1T(n + 1, n) | 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 |
Std | DiagRow2T(n + 2, n) | A080663 | 2 11 26 47 74 107 146 191 242 299 362 431 506 587 674 767 866 971 1082 1199 1322 1451 1586 1727 |
Std | DiagRow3T(n + 3, n) | A165676 | 6 50 154 342 638 1066 1650 2414 3382 4578 6026 7750 9774 12122 14818 17886 21350 25234 29562 34358 |
Std | DiagCol1T(n + 1, 1) | A000254 | 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
Std | DiagCol2T(n + 2, 2) | A001705 | 1 5 26 154 1044 8028 69264 663696 6999840 80627040 1007441280 13575738240 196287356160 |
Std | DiagCol3T(n + 3, 3) | A001711 | 1 7 47 342 2754 24552 241128 2592720 30334320 383970240 5231113920 76349105280 1188825724800 |
Std | Polysee docs | missing | 1 1 1 2 2 1 6 6 3 1 24 23 12 4 1 120 108 56 20 5 1 720 605 300 111 30 6 1 5040 3956 1836 678 194 42 |
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 | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 6 23 56 111 194 311 468 671 926 1239 1616 2063 2586 3191 3884 4671 5558 6551 7656 8879 10226 11703 |
Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 12 56 300 1836 12760 99912 873696 8458976 89952192 1043100480 13107099904 177471036672 |
Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 20 111 678 4569 34038 280197 2541654 25295193 274793742 3241326429 41300996526 565775501697 |
Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 12 111 1344 19965 350856 7117677 163705344 4209578829 119679019200 3727636057101 |
Alt | TriangleT(n, k), 0 ≤ k ≤ n | A165675 | 1 1 -1 2 -3 1 6 -11 5 -1 24 -50 26 -7 1 120 -274 154 -47 9 -1 720 -1764 1044 -342 74 -11 1 5040 |
Alt | RevT(n, n - k), 0 ≤ k ≤ n | A105954 | 1 -1 1 1 -3 2 -1 5 -11 6 1 -7 26 -50 24 -1 9 -47 154 -274 120 1 -11 74 -342 1044 -1764 720 -1 13 |
Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -5 3 1 8 -4 -5 1 112 -56 -61 7 1 -256 128 160 -16 -9 1 -5632 2816 3520 -352 -173 11 1 18432 |
Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 3 -5 1 -5 -4 8 1 7 -61 -56 112 1 -9 -16 160 128 -256 1 11 -173 -352 3520 2816 -5632 1 -13 |
Alt | Accsee docs | missing | 1 1 0 2 -1 0 6 -5 0 -1 24 -26 0 -7 -6 120 -154 0 -47 -38 -39 720 -1044 0 -342 -268 -279 -278 5040 |
Alt | AccRevsee docs | missing | 1 -1 0 1 -2 0 -1 4 -7 -1 1 -6 20 -30 -6 -1 8 -39 115 -159 -39 1 -10 64 -278 766 -998 -278 -1 12 -95 |
Alt | AntiDiagsee docs | missing | 1 1 2 -1 6 -3 24 -11 1 120 -50 5 720 -274 26 -1 5040 -1764 154 -7 40320 -13068 1044 -47 1 362880 |
Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 2 -6 3 6 -22 15 -4 24 -100 78 -28 5 120 -548 462 -188 45 -6 720 -3528 3132 -1368 370 -66 7 |
Alt | RowSum∑ k=0..n T(n, k) | missing | 1 0 0 -1 -6 -39 -278 -2211 -19542 -190711 -2040606 -23781627 -300064094 -4077048063 -59369465814 |
Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 11 51 283 1839 13719 115675 1088459 11311047 128686087 1591143315 21247786347 304787011135 |
Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -3 -12 -57 -322 -2117 -15930 -135217 -1279170 -13351653 -152467714 -1891207409 -25324834410 |
Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A093345 | 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 |
Alt | AbsSum∑ k=0..n | T(n, k) | | A093345 | 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 |
Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 3 14 75 471 3423 28250 260991 2668807 29927931 365222310 4818671403 68353290631 1037408256255 |
Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 1 0 -15 -158 -1491 -14502 -150391 -1677726 -20152827 -260147294 -3598046463 -53142445014 |
Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -1 -5 -21 -115 -733 -5397 -45029 -420095 -4334445 -49013857 -602850853 -8013275931 |
Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 330 54600 178489080 7911786960 839338855795440 11191805812769662080 |
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) | | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
Alt | ColMiddleT(n, n // 2) | missing | 1 1 -3 -11 26 154 -342 -2754 5944 60216 -127860 -1557660 3272688 46536624 -97053936 -1576890000 |
Alt | CentralET(2 n, n) | missing | 1 -3 26 -342 5944 -127860 3272688 -97053936 3270729600 -123418922400 5154170774400 -235977273544320 |
Alt | CentralOT(2 n + 1, n) | missing | 1 -11 154 -2754 60216 -1557660 46536624 -1576890000 59753750400 -2503748556000 114942011990400 |
Alt | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 -13 -47 -136 1 5935 88481 1060568 11963541 131894883 1423461073 14655258656 132538911961 |
Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 9 -55 409 -3546 34981 -386163 4711281 -62903242 911810321 -14254347735 238977876457 |
Alt | TransNat0∑ k=0..n T(n, k) k | A002467 | 0 -1 -1 -4 -15 -76 -455 -3186 -25487 -229384 -2293839 -25232230 -302786759 -3936227868 -55107190151 |
Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -1 -5 -21 -115 -733 -5397 -45029 -420095 -4334445 -49013857 -602850853 -8013275931 |
Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 1 0 7 38 279 2210 19543 190710 2040607 23781626 300064095 4077048062 59369465815 922613088258 |
Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 3 13 75 517 3875 26301 29531 -5729003 -227270157 -7253745395 -223673532181 -7005519261531 |
Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 15 -103 903 -9663 122287 -1787991 29671479 -551104591 11328415263 -255351604647 6263220826471 |
Alt | DiagRow1T(n + 1, n) | 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 |
Alt | DiagRow2T(n + 2, n) | A080663 | 2 -11 26 -47 74 -107 146 -191 242 -299 362 -431 506 -587 674 -767 866 -971 1082 -1199 1322 -1451 |
Alt | DiagRow3T(n + 3, n) | A165676 | 6 -50 154 -342 638 -1066 1650 -2414 3382 -4578 6026 -7750 9774 -12122 14818 -17886 21350 -25234 |
Alt | DiagCol1T(n + 1, 1) | A000254 | -1 -3 -11 -50 -274 -1764 -13068 -109584 -1026576 -10628640 -120543840 -1486442880 -19802759040 |
Alt | DiagCol2T(n + 2, 2) | A001705 | 1 5 26 154 1044 8028 69264 663696 6999840 80627040 1007441280 13575738240 196287356160 |
Alt | DiagCol3T(n + 3, 3) | A001711 | -1 -7 -47 -342 -2754 -24552 -241128 -2592720 -30334320 -383970240 -5231113920 -76349105280 |
Alt | Polysee docs | missing | 1 1 1 2 0 1 6 0 -1 1 24 -1 0 -2 1 120 -6 -4 2 -3 1 720 -39 -12 -9 6 -4 1 5040 -278 -76 0 -22 12 -5 |
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 | 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 |
Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 6 -1 -4 -9 -22 -49 -96 -169 -274 -417 -604 -841 -1134 -1489 -1912 -2409 -2986 -3649 -4404 -5257 |
Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 0 -4 -12 -76 -472 -3528 -29536 -276832 -2866368 -32512576 -400954624 -5342062848 -76474349056 |
Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 2 -9 0 -99 -360 -3303 -25344 -239139 -2431728 -27329535 -333808776 -4411360683 -62688272328 |
Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 -9 48 -775 10872 -198303 4034816 -93836151 2429006400 -69522690127 2177588261376 |
Rev | TriangleT(n, k), 0 ≤ k ≤ n | A105954 | 1 1 1 1 3 2 1 5 11 6 1 7 26 50 24 1 9 47 154 274 120 1 11 74 342 1044 1764 720 1 13 107 638 2754 |
Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 1 -3 1 0 4 -5 1 0 0 9 -7 1 0 0 0 16 -9 1 0 0 0 0 25 -11 1 0 0 0 0 0 36 -13 1 0 0 0 0 0 0 49 |
Rev | Accsee docs | missing | 1 1 2 1 4 6 1 6 17 23 1 8 34 84 108 1 10 57 211 485 605 1 12 86 428 1472 3236 3956 1 14 121 759 |
Rev | AccRevsee docs | missing | 1 1 2 2 5 6 6 17 22 23 24 74 100 107 108 120 394 548 595 604 605 720 2484 3528 3870 3944 3955 3956 |
Rev | AntiDiagsee docs | missing | 1 1 1 1 1 3 1 5 2 1 7 11 1 9 26 6 1 11 47 50 1 13 74 154 24 1 15 107 342 274 1 17 146 638 1044 120 |
Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 6 6 1 10 33 24 1 14 78 200 120 1 18 141 616 1370 720 1 22 222 1368 5220 10584 5040 1 26 321 |
Rev | RowSum∑ k=0..n T(n, k) | A093345 | 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 |
Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 12 51 322 1839 15930 115675 1279170 11311047 152467714 1591143315 25324834410 304787011135 |
Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 3 11 57 283 2117 13719 135217 1088459 13351653 128686087 1891207409 21247786347 364156476949 |
Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 0 0 1 -6 39 -278 2211 -19542 190711 -2040606 23781627 -300064094 4077048063 -59369465814 |
Rev | AbsSum∑ k=0..n | T(n, k) | | A093345 | 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 |
Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 4 8 19 42 109 266 739 1966 5795 16606 51631 157814 515203 1666726 5691287 19366846 68939899 |
Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 11 47 235 1369 9191 70207 602755 5753597 60495199 695039491 8665989227 116564043985 |
Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 13 68 413 2866 22457 196634 1906165 20290322 235457201 2959959922 40086920909 582025267370 |
Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 330 54600 178489080 7911786960 839338855795440 11191805812769662080 |
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) | | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
Rev | ColMiddleT(n, n // 2) | missing | 1 1 3 5 26 47 342 638 5944 11274 127860 245004 3272688 6314664 97053936 188204400 3270729600 |
Rev | CentralET(2 n, n) | missing | 1 3 26 342 5944 127860 3272688 97053936 3270729600 123418922400 5154170774400 235977273544320 |
Rev | CentralOT(2 n + 1, n) | A058806 | 1 5 47 638 11274 245004 6314664 188204400 6366517200 240947474400 10086271796160 462688566802560 |
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) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 9 55 409 3546 34981 386163 4711281 62903242 911810321 14254347735 238977876457 4275994190482 |
Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -3 -13 -47 -136 1 5935 88481 1060568 11963541 131894883 1423461073 14655258656 132538911961 |
Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 7 45 305 2261 18501 166985 1655273 17922693 210794501 2678806121 36604570185 535452646613 |
Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 13 68 413 2866 22457 196634 1906165 20290322 235457201 2959959922 40086920909 582025267370 |
Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 11 103 945 8967 90109 968355 11162697 137997271 1826219517 25806039699 388296685225 |
Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 12 56 300 1836 12760 99912 873696 8458976 89952192 1043100480 13107099904 177471036672 |
Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 0 -4 -12 -76 -472 -3528 -29536 -276832 -2866368 -32512576 -400954624 -5342062848 -76474349056 |
Rev | DiagRow1T(n + 1, n) | A000254 | 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
Rev | DiagRow2T(n + 2, n) | A001705 | 1 5 26 154 1044 8028 69264 663696 6999840 80627040 1007441280 13575738240 196287356160 |
Rev | DiagRow3T(n + 3, n) | A001711 | 1 7 47 342 2754 24552 241128 2592720 30334320 383970240 5231113920 76349105280 1188825724800 |
Rev | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A080663 | 2 11 26 47 74 107 146 191 242 299 362 431 506 587 674 767 866 971 1082 1199 1322 1451 1586 1727 |
Rev | DiagCol3T(n + 3, 3) | A165676 | 6 50 154 342 638 1066 1650 2414 3382 4578 6026 7750 9774 12122 14818 17886 21350 25234 29562 34358 |
Rev | Polysee docs | missing | 1 1 1 1 2 1 1 6 3 1 1 23 15 4 1 1 108 103 28 5 1 1 605 903 277 45 6 1 1 3956 9663 3550 581 66 7 1 1 |
Rev | 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 |
Rev | PolyRow2∑ k=0..2 T(2, 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 | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 23 103 277 581 1051 1723 2633 3817 5311 7151 9373 12013 15107 18691 22801 27473 32743 38647 45221 |
Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 15 103 903 9663 122287 1787991 29671479 551104591 11328415263 255351604647 6263220826471 |
Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 28 277 3550 55963 1048030 22741159 561170926 15520809643 475592544598 15993601630975 |
Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 15 277 9789 566721 48738811 5829856971 925258217721 188084091286261 47643226823678391 |
Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -3 1 0 4 -5 1 0 0 9 -7 1 0 0 0 16 -9 1 0 0 0 0 25 -11 1 0 0 0 0 0 36 -13 1 0 0 0 0 0 0 49 |
Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 1 1 -5 4 0 1 -7 9 0 0 1 -9 16 0 0 0 1 -11 25 0 0 0 0 1 -13 36 0 0 0 0 0 1 -15 49 0 0 0 |
Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A105954 | 1 1 1 1 3 2 1 5 11 6 1 7 26 50 24 1 9 47 154 274 120 1 11 74 342 1044 1764 720 1 13 107 638 2754 |
Inv | Accsee docs | missing | 1 -1 0 1 -2 -1 0 4 -1 0 0 0 9 2 3 0 0 0 16 7 8 0 0 0 0 25 14 15 0 0 0 0 0 36 23 24 0 0 0 0 0 0 49 |
Inv | AccRevsee docs | missing | 1 1 0 1 -2 -1 1 -4 0 0 1 -6 3 3 3 1 -8 8 8 8 8 1 -10 15 15 15 15 15 1 -12 24 24 24 24 24 24 1 -14 |
Inv | AntiDiagsee docs | missing | 1 -1 1 1 0 -3 0 4 1 0 0 -5 0 0 9 1 0 0 0 -7 0 0 0 16 1 0 0 0 0 -9 0 0 0 0 25 1 0 0 0 0 0 -11 0 0 0 |
Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -6 3 0 8 -15 4 0 0 27 -28 5 0 0 0 64 -45 6 0 0 0 0 125 -66 7 0 0 0 0 0 216 -91 8 0 0 0 0 0 |
Inv | RowSum∑ k=0..n T(n, k) | A005563 | 1 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 |
Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 2 -5 10 -9 26 -13 50 -17 82 -21 122 -25 170 -29 226 -33 290 -37 362 -41 442 -45 530 -49 626 |
Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -3 5 -7 17 -11 37 -15 65 -19 101 -23 145 -27 197 -31 257 -35 325 -39 401 -43 485 -47 577 -51 |
Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A002522 | 1 -2 5 -10 17 -26 37 -50 65 -82 101 -122 145 -170 197 -226 257 -290 325 -362 401 -442 485 -530 577 |
Inv | AbsSum∑ k=0..n | T(n, k) | | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 2 -3 5 -5 10 -7 17 -9 26 -11 37 -13 50 -15 65 -17 82 -19 101 -21 122 -23 145 -25 170 -27 197 |
Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -2 3 14 31 54 83 118 159 206 259 318 383 454 531 614 703 798 899 1006 1119 1238 1363 1494 1631 |
Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -2 -3 4 25 66 133 232 369 550 781 1068 1417 1834 2325 2896 3553 4302 5149 6100 7161 8338 9637 |
Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | A099721 | 1 1 3 20 63 144 275 468 735 1088 1539 2100 2783 3600 4563 5684 6975 8448 10115 11988 14079 16400 |
Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 5 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -3 4 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | CentralET(2 n, n) | missing | 1 -3 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Inv | CentralOT(2 n + 1, n) | A261595 | -1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Inv | ColLeftT(n, 0) | A115944 | 1 -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 |
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 -4 -2 27 116 310 666 1253 2152 3456 5270 7711 10908 15002 20146 26505 34256 43588 54702 67811 |
Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 8 28 83 206 442 848 1493 2458 3836 5732 8263 11558 15758 21016 27497 35378 44848 56108 69371 |
Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -1 -3 1 17 51 109 197 321 487 701 969 1297 1691 2157 2701 3329 4047 4861 5777 6801 7939 9197 |
Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -2 -3 4 25 66 133 232 369 550 781 1068 1417 1834 2325 2896 3553 4302 5149 6100 7161 8338 9637 |
Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 1 -7 -11 25 161 481 1093 2129 3745 6121 9461 13993 19969 27665 37381 49441 64193 82009 103285 |
Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A073577 | 1 -1 -1 7 23 47 79 119 167 223 287 359 439 527 623 727 839 959 1087 1223 1367 1519 1679 1847 2023 |
Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A164897 | 1 3 11 27 51 83 123 171 227 291 363 443 531 627 731 843 963 1091 1227 1371 1523 1683 1851 2027 2211 |
Inv | DiagRow1T(n + 1, n) | 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 |
Inv | DiagRow2T(n + 2, n) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
Inv | DiagCol1T(n + 1, 1) | missing | 1 -3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | DiagCol2T(n + 2, 2) | missing | 1 -5 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -7 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 1 1 0 1 0 -1 1 1 0 0 -1 2 1 0 3 -4 1 3 1 0 8 -4 -6 5 4 1 0 15 16 -27 0 11 5 1 0 24 112 -54 -48 |
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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 0 -4 -6 0 20 60 126 224 360 540 770 1056 1404 1820 2310 2880 3536 4284 5130 6080 7140 8316 9614 |
Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 -4 -4 16 112 448 1472 4352 12032 31744 80896 200704 487424 1163264 2736128 6356992 14614528 |
Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 1 -6 -27 -54 81 1458 9477 48114 216513 905418 3601989 13817466 51549777 188130114 674398629 |
Inv | PolyDiag∑ k=0..n T(n, k) n^k | A053506 | 1 0 -1 -6 -48 -500 -6480 -100842 -1835008 -38263752 -900000000 -23579476910 -681091006464 |
Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -3 1 1 -5 4 0 1 -7 9 0 0 1 -9 16 0 0 0 1 -11 25 0 0 0 0 1 -13 36 0 0 0 0 0 1 -15 49 0 0 0 |
Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -3 1 0 4 -5 1 0 0 9 -7 1 0 0 0 16 -9 1 0 0 0 0 25 -11 1 0 0 0 0 0 36 -13 1 0 0 0 0 0 0 49 |
Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A165675 | 1 1 1 2 3 1 6 11 5 1 24 50 26 7 1 120 274 154 47 9 1 720 1764 1044 342 74 11 1 5040 13068 8028 2754 |
Inv:Rev | Accsee docs | missing | 1 1 0 1 -2 -1 1 -4 0 0 1 -6 3 3 3 1 -8 8 8 8 8 1 -10 15 15 15 15 15 1 -12 24 24 24 24 24 24 1 -14 |
Inv:Rev | AccRevsee docs | missing | 1 -1 0 1 -2 -1 0 4 -1 0 0 0 9 2 3 0 0 0 16 7 8 0 0 0 0 25 14 15 0 0 0 0 0 36 23 24 0 0 0 0 0 0 49 |
Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -3 1 -5 1 1 -7 4 1 -9 9 0 1 -11 16 0 1 -13 25 0 0 1 -15 36 0 0 1 -17 49 0 0 0 1 -19 64 0 |
Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -6 3 1 -10 12 0 1 -14 27 0 0 1 -18 48 0 0 0 1 -22 75 0 0 0 0 1 -26 108 0 0 0 0 0 1 -30 147 |
Inv:Rev | RowSum∑ k=0..n T(n, k) | A005563 | 1 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 |
Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A002522 | 1 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 |
Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A005408 | 0 -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 | AltSum∑ k=0..n T(n, k) (-1)^k | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A002522 | 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 |
Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -2 -3 4 25 66 133 232 369 550 781 1068 1417 1834 2325 2896 3553 4302 5149 6100 7161 8338 9637 |
Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -2 3 14 31 54 83 118 159 206 259 318 383 454 531 614 703 798 899 1006 1119 1238 1363 1494 1631 |
Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A099721 | 1 1 3 20 63 144 275 468 735 1088 1539 2100 2783 3600 4563 5684 6975 8448 10115 11988 14079 16400 |
Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 3 5 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -3 -5 9 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | CentralET(2 n, n) | missing | 1 -3 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -5 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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) | A115944 | 1 -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 |
Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -2 27 116 310 666 1253 2152 3456 5270 7711 10908 15002 20146 26505 34256 43588 54702 67811 |
Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 8 -28 83 -206 442 -848 1493 -2458 3836 -5732 8263 -11558 15758 -21016 27497 -35378 44848 |
Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A142463 | 0 -1 -1 3 11 23 39 59 83 111 143 179 219 263 311 363 419 479 543 611 683 759 839 923 1011 1103 1199 |
Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -2 3 14 31 54 83 118 159 206 259 318 383 454 531 614 703 798 899 1006 1119 1238 1363 1494 1631 |
Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A082108 | 0 -1 1 11 29 55 89 131 181 239 305 379 461 551 649 755 869 991 1121 1259 1405 1559 1721 1891 2069 |
Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 -4 -4 16 112 448 1472 4352 12032 31744 80896 200704 487424 1163264 2736128 6356992 14614528 |
Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 11 -36 108 -304 816 -2112 5312 -13056 31488 -74752 175104 -405504 929792 -2113536 4767744 |
Inv:Rev | DiagRow1T(n + 1, n) | missing | 1 -3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | DiagRow2T(n + 2, n) | missing | 1 -5 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -7 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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) | 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 |
Inv:Rev | DiagCol2T(n + 2, 2) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 0 -1 -2 1 1 3 7 1 -3 1 1 8 23 22 5 -4 1 1 15 47 61 45 11 -5 1 1 24 79 118 |
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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A033954 | 1 0 7 22 45 76 115 162 217 280 351 430 517 612 715 826 945 1072 1207 1350 1501 1660 1827 2002 2185 |
Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A073577 | 1 -1 -1 7 23 47 79 119 167 223 287 359 439 527 623 727 839 959 1087 1223 1367 1519 1679 1847 2023 |
Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 1 22 61 118 193 286 397 526 673 838 1021 1222 1441 1678 1933 2206 2497 2806 3133 3478 3841 |
Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 22 117 356 835 1674 3017 5032 7911 11870 17149 24012 32747 43666 57105 73424 93007 116262 |
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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.