GENOCCHI[0] 1
[1] 1, 1
[2] 2, 3, 3
[3] 8, 14, 17, 17
[4] 56, 104, 138, 155, 155
[5] 608, 1160, 1608, 1918, 2073, 2073

      OEIS Similars: A297703

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA2977031 1 1 2 3 3 8 14 17 17 56 104 138 155 155 608 1160 1608 1918 2073 2073 9440 18272 25944 32008 36154
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 1 3 3 2 17 17 14 8 155 155 138 104 56 2073 2073 1918 1608 1160 608 38227 38227 36154 32008
StdAccsee docsmissing1 1 2 2 5 8 8 22 39 56 56 160 298 453 608 608 1768 3376 5294 7367 9440 9440 27712 53656 85664
StdAccRevsee docsmissing1 1 2 3 6 8 17 34 48 56 155 310 448 552 608 2073 4146 6064 7672 8832 9440 38227 76454 112608 144616
StdAntiDiagsee docsmissing1 1 2 1 8 3 56 14 3 608 104 17 9440 1160 138 17 198272 18272 1608 155 5410688 387104 25944 1918 155
StdDiffx1T(n, k) (k+1)missing1 1 2 2 6 9 8 28 51 68 56 208 414 620 775 608 2320 4824 7672 10365 12438 9440 36544 77832 128032
StdRowSum k=0..n T(n, k)A0054391 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920 1721379917619200
StdEvenSum k=0..n T(n, k) even(k)missing1 1 5 25 349 4289 109765 2500393 100852205 3681669649 214553157013 11472607401593 911390528780989
StdOddSum k=0..n T(n, k) odd(k)missing0 1 3 31 259 5151 88507 2910295 85191699 4186069999 186740681323 12817906344327 809989388838211
StdAltSum k=0..n T(n, k) (-1)^kmissing1 0 2 -6 90 -862 21258 -409902 15660506 -504400350 27812475690 -1345298942734 101401139942778
StdAbsSum k=0..n | T(n, k) |A0054391 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920 1721379917619200
StdDiagSum k=0..n // 2 T(n - k, k)missing1 1 3 11 73 729 10755 218307 5825809 197258753 8250605691 417400530139 25108813596889
StdAccSum k=0..n j=0..k T(n, j)missing1 3 15 125 1575 27853 656607 19875573 750786135 34601854397 1910375017551 124447006212997
StdAccRevSum k=0..n j=0..k T(n, n - j)A1105011 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 6 952 7785960 11742600707040 48330376367013905045280 1394963925815260169445240796533120
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdRowMaxMax k=0..n | T(n, k) |A1105011 1 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
StdColMiddleT(n, n // 2)missing1 1 3 14 138 1608 32008 702280 23281432 826094560 40990855776 2142617789472 148530446419808
StdCentralET(2 n, n)missing1 3 138 32008 23281432 40990855776 148530446419808 990793141677516416 11215719940701859747200
StdCentralOT(2 n + 1, n)missing1 14 1608 702280 826094560 2142617789472 10739019716120192 94695920709718106240
StdColLeftT(n, 0)A0054391 1 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920
StdColRightT(n, n)A1105011 1 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
StdBinConv k=0..n C(n, k) T(n, k)missing1 2 11 118 2075 54106 1958291 93874558 5754873035 439059245986 40790951673251 4533473402322118
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0369681 0 -1 0 3 0 -17 0 155 0 -2073 0 38227 0 -929569 0 28820619 0 -1109652905 0 51943281731 0
StdTransNat0 k=0..n T(n, k) kmissing0 1 9 99 1465 28787 731297 23409931 923609001 44075542083 2503857204145 167039158738043
StdTransNat1 k=0..n T(n, k) (k + 1)A1105011 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
StdTransSqrs k=0..n T(n, k) k^2missing0 1 15 235 4531 109847 3320431 123273403 5533969803 296088979327 18638740323559 1364772490606595
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 3 17 171 2745 64771 2119329 92108379 5143290377 359335100979 30736977912561 3161546060955787
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -1 5 -25 461 -8161 284885 -11096233 630154589 -42245508337 3616785941861 -365905646032057
StdDiagRow1T(n + 1, n)A1105011 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
StdDiagRow2T(n + 2, n)missing2 14 138 1918 36154 891342 27891050 1080832286 50833628826 2853207760750 188424521441482
StdDiagRow3T(n + 3, n)missing8 104 1608 32008 814888 26031912 1023191048 48614323016 2749321197288 182614219356520
StdDiagCol1T(n + 1, 1)missing1 3 14 104 1160 18272 387104 10623104 366677120 15549435392 794719937024 48179733653504
StdDiagCol2T(n + 2, 2)missing3 17 138 1608 25944 557664 15448416 536687232 22864454016 1172596600320 71274233624064
StdDiagCol3T(n + 3, 3)missing17 155 1918 32008 702280 19716064 691248928 29642785408 1527608809600 93196136994304
StdPolysee docsmissing1 1 1 2 2 1 8 8 3 1 56 56 20 4 1 608 608 240 38 5 1 9440 9440 4536 662 62 6 1 198272 198272 124208
StdPolyRow1 k=0..1 T(1, k) n^kA0000271 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
StdPolyRow2 k=0..2 T(2, k) n^kA0775882 8 20 38 62 92 128 170 218 272 332 398 470 548 632 722 818 920 1028 1142 1262 1388 1520 1658 1802
StdPolyRow3 k=0..3 T(3, k) n^kmissing8 56 240 662 1424 2628 4376 6770 9912 13904 18848 24846 32000 40412 50184 61418 74216 88680 104912
StdPolyCol2 k=0..n T(n, k) 2^kmissing1 3 20 240 4536 124208 4654080 228859776 14303848064 1107862922496 104171982879744
StdPolyCol3 k=0..n T(n, k) 3^kmissing1 4 38 662 18350 741998 41247086 3018565358 281375550542 32550962041742 4576387009804334
StdPolyDiag k=0..n T(n, k) n^kmissing1 2 20 662 52280 8060108 2135594432 892111352906 552241988561792 483443881772422040
AltTriangleT(n, k), 0 ≤ k ≤ nA2977031 1 -1 2 -3 3 8 -14 17 -17 56 -104 138 -155 155 608 -1160 1608 -1918 2073 -2073 9440 -18272 25944
AltRevT(n, n - k), 0 ≤ k ≤ nmissing1 -1 1 3 -3 2 -17 17 -14 8 155 -155 138 -104 56 -2073 2073 -1918 1608 -1160 608 38227 -38227 36154
AltAccsee docsmissing1 1 0 2 -1 2 8 -6 11 -6 56 -48 90 -65 90 608 -552 1056 -862 1211 -862 9440 -8832 17112 -14896 21258
AltAccRevsee docsmissing1 -1 0 3 0 2 -17 0 -14 -6 155 0 138 34 90 -2073 0 -1918 -310 -1470 -862 38227 0 36154 4146 30090
AltAntiDiagsee docsmissing1 1 2 -1 8 -3 56 -14 3 608 -104 17 9440 -1160 138 -17 198272 -18272 1608 -155 5410688 -387104 25944
AltDiffx1T(n, k) (k+1)missing1 1 -2 2 -6 9 8 -28 51 -68 56 -208 414 -620 775 608 -2320 4824 -7672 10365 -12438 9440 -36544 77832
AltRowSum k=0..n T(n, k)missing1 0 2 -6 90 -862 21258 -409902 15660506 -504400350 27812475690 -1345298942734 101401139942778
AltEvenSum k=0..n T(n, k) even(k)missing1 1 5 25 349 4289 109765 2500393 100852205 3681669649 214553157013 11472607401593 911390528780989
AltOddSum k=0..n T(n, k) odd(k)missing0 -1 -3 -31 -259 -5151 -88507 -2910295 -85191699 -4186069999 -186740681323 -12817906344327
AltAltSum k=0..n T(n, k) (-1)^kA0054391 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920 1721379917619200
AltAbsSum k=0..n | T(n, k) |A0054391 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920 1721379917619200
AltDiagSum k=0..n // 2 T(n - k, k)missing1 1 1 5 45 521 8401 181453 5047765 175948529 7515842745 386262150773 23517989442301
AltAccSum k=0..n j=0..k T(n, j)missing1 1 3 7 123 599 28371 226127 20685931 243294119 36523762819 594001273599 132661391814427
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -1 5 -37 417 -6633 141693 -3915245 135919129 -5791697969 297225945461 -18082887529141
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 6 952 7785960 11742600707040 48330376367013905045280 1394963925815260169445240796533120
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltRowMaxMax k=0..n | T(n, k) |A1105011 1 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
AltColMiddleT(n, n // 2)missing1 1 -3 -14 138 1608 -32008 -702280 23281432 826094560 -40990855776 -2142617789472 148530446419808
AltCentralET(2 n, n)missing1 -3 138 -32008 23281432 -40990855776 148530446419808 -990793141677516416 11215719940701859747200
AltCentralOT(2 n + 1, n)missing1 -14 1608 -702280 826094560 -2142617789472 10739019716120192 -94695920709718106240
AltColLeftT(n, 0)A0054391 1 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920
AltColRightT(n, n)A1105011 -1 3 -17 155 -2073 38227 -929569 28820619 -1109652905 51943281731 -2905151042481 191329672483963
AltBinConv k=0..n C(n, k) T(n, k)A0369681 0 -1 0 3 0 -17 0 155 0 -2073 0 38227 0 -929569 0 28820619 0 -1109652905 0 51943281731 0
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -2 11 -118 2075 -54106 1958291 -93874558 5754873035 -439059245986 40790951673251
AltTransNat0 k=0..n T(n, k) kmissing0 -1 3 -31 327 -5771 120435 -3505343 120258623 -5287297619 269413469771 -16737588586407
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -1 5 -37 417 -6633 141693 -3915245 135919129 -5791697969 297225945461 -18082887529141
AltTransSqrs k=0..n T(n, k) k^2missing0 -1 9 -99 1533 -30647 796393 -25806707 1031818181 -49655128255 2845513230641 -190981905325755
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 1 5 25 461 8161 284885 11096233 630154589 42245508337 3616785941861 365905646032057
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -3 17 -171 2745 -64771 2119329 -92108379 5143290377 -359335100979 30736977912561
AltDiagRow1T(n + 1, n)A1105011 -3 17 -155 2073 -38227 929569 -28820619 1109652905 -51943281731 2905151042481 -191329672483963
AltDiagRow2T(n + 2, n)missing2 -14 138 -1918 36154 -891342 27891050 -1080832286 50833628826 -2853207760750 188424521441482
AltDiagRow3T(n + 3, n)missing8 -104 1608 -32008 814888 -26031912 1023191048 -48614323016 2749321197288 -182614219356520
AltDiagCol1T(n + 1, 1)missing-1 -3 -14 -104 -1160 -18272 -387104 -10623104 -366677120 -15549435392 -794719937024 -48179733653504
AltDiagCol2T(n + 2, 2)missing3 17 138 1608 25944 557664 15448416 536687232 22864454016 1172596600320 71274233624064
AltDiagCol3T(n + 3, 3)missing-17 -155 -1918 -32008 -702280 -19716064 -691248928 -29642785408 -1527608809600 -93196136994304
AltPolysee docsmissing1 1 1 2 0 1 8 2 -1 1 56 -6 8 -2 1 608 90 -88 20 -3 1 9440 -862 1640 -340 38 -4 1 198272 21258
AltPolyRow1 k=0..1 T(1, k) n^kA0000271 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
AltPolyRow2 k=0..2 T(2, k) n^kA0775882 2 8 20 38 62 92 128 170 218 272 332 398 470 548 632 722 818 920 1028 1142 1262 1388 1520 1658
AltPolyRow3 k=0..3 T(3, k) n^kmissing8 -6 -88 -340 -864 -1762 -3136 -5088 -7720 -11134 -15432 -20716 -27088 -34650 -43504 -53752 -65496
AltPolyCol2 k=0..n T(n, k) 2^kmissing1 -1 8 -88 1640 -43792 1622336 -78940672 4901777792 -377651569408 35376898617344 -3958593435437056
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -2 20 -340 9356 -376012 20830700 -1520807404 141534247724 -16354424297644 2297333169378284
AltPolyDiag k=0..n T(n, k) n^kmissing1 0 8 -340 31608 -5387242 1527041408 -669417486552 429633164403584 -386811585079956982
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 1 3 3 2 17 17 14 8 155 155 138 104 56 2073 2073 1918 1608 1160 608 38227 38227 36154 32008
RevAccsee docsmissing1 1 2 3 6 8 17 34 48 56 155 310 448 552 608 2073 4146 6064 7672 8832 9440 38227 76454 112608 144616
RevAccRevsee docsmissing1 1 2 2 5 8 8 22 39 56 56 160 298 453 608 608 1768 3376 5294 7367 9440 9440 27712 53656 85664
RevAntiDiagsee docsmissing1 1 3 1 17 3 155 17 2 2073 155 14 38227 2073 138 8 929569 38227 1918 104 28820619 929569 36154 1608
RevDiffx1T(n, k) (k+1)missing1 1 2 3 6 6 17 34 42 32 155 310 414 416 280 2073 4146 5754 6432 5800 3648 38227 76454 108462 128032
RevRowSum k=0..n T(n, k)A0054391 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920 1721379917619200
RevEvenSum k=0..n T(n, k) even(k)missing1 1 5 31 349 5151 109765 2910295 100852205 4186069999 214553157013 12817906344327 911390528780989
RevOddSum k=0..n T(n, k) odd(k)missing0 1 3 25 259 4289 88507 2500393 85191699 3681669649 186740681323 11472607401593 809989388838211
RevAltSum k=0..n T(n, k) (-1)^kmissing1 0 2 6 90 862 21258 409902 15660506 504400350 27812475690 1345298942734 101401139942778
RevAbsSum k=0..n | T(n, k) |A0054391 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920 1721379917619200
RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 4 20 174 2242 40446 969818 29788006 1139398034 53081667126 2958201908962 194286704194854
RevAccSum k=0..n j=0..k T(n, j)A1105011 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
RevAccRevSum k=0..n j=0..k T(n, n - j)missing1 3 15 125 1575 27853 656607 19875573 750786135 34601854397 1910375017551 124447006212997
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 6 952 7785960 11742600707040 48330376367013905045280 1394963925815260169445240796533120
RevRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevRowMaxMax k=0..n | T(n, k) |A1105011 1 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
RevColMiddleT(n, n // 2)missing1 1 3 17 138 1918 32008 814888 23281432 937658760 40990855776 2391266489696 148530446419808
RevCentralET(2 n, n)missing1 3 138 32008 23281432 40990855776 148530446419808 990793141677516416 11215719940701859747200
RevCentralOT(2 n + 1, n)missing1 17 1918 814888 937658760 2391266489696 11829206389864736 103230184431408446592
RevColLeftT(n, 0)A1105011 1 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
RevColRightT(n, n)A0054391 1 2 8 56 608 9440 198272 5410688 186043904 7867739648 401293838336 24290513745920
RevBinConv k=0..n C(n, k) T(n, k)missing1 2 11 118 2075 54106 1958291 93874558 5754873035 439059245986 40790951673251 4533473402322118
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0369681 0 -1 0 3 0 -17 0 155 0 -2073 0 38227 0 -929569 0 28820619 0 -1109652905 0 51943281731 0
RevTransNat0 k=0..n T(n, k) kmissing0 1 7 69 967 18413 458335 14464885 564742231 26734114749 1509081179215 100156492467077
RevTransNat1 k=0..n T(n, k) (k + 1)missing1 3 15 125 1575 27853 656607 19875573 750786135 34601854397 1910375017551 124447006212997
RevTransSqrs k=0..n T(n, k) k^2missing0 1 11 145 2539 57977 1682659 60658081 2663035643 140016133321 8690980074259 629063161625969
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 3 20 240 4536 124208 4654080 228859776 14303848064 1107862922496 104171982879744
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -1 8 -88 1640 -43792 1622336 -78940672 4901777792 -377651569408 35376898617344 -3958593435437056
RevDiagRow1T(n + 1, n)missing1 3 14 104 1160 18272 387104 10623104 366677120 15549435392 794719937024 48179733653504
RevDiagRow2T(n + 2, n)missing3 17 138 1608 25944 557664 15448416 536687232 22864454016 1172596600320 71274233624064
RevDiagRow3T(n + 3, n)missing17 155 1918 32008 702280 19716064 691248928 29642785408 1527608809600 93196136994304
RevDiagCol1T(n + 1, 1)A1105011 3 17 155 2073 38227 929569 28820619 1109652905 51943281731 2905151042481 191329672483963
RevDiagCol2T(n + 2, 2)missing2 14 138 1918 36154 891342 27891050 1080832286 50833628826 2853207760750 188424521441482
RevDiagCol3T(n + 3, 3)missing8 104 1608 32008 814888 26031912 1023191048 48614323016 2749321197288 182614219356520
RevPolysee docsmissing1 1 1 3 2 1 17 8 3 1 155 56 17 4 1 2073 608 171 30 5 1 38227 9440 2745 410 47 6 1 929569 198272
RevPolyRow1 k=0..1 T(1, k) n^kA0000271 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
RevPolyRow2 k=0..2 T(2, k) n^kA0338163 8 17 30 47 68 93 122 155 192 233 278 327 380 437 498 563 632 705 782 863 948 1037 1130 1227 1328
RevPolyRow3 k=0..3 T(3, k) n^kmissing17 56 171 410 821 1452 2351 3566 5145 7136 9587 12546 16061 20180 24951 30422 36641 43656 51515
RevPolyCol2 k=0..n T(n, k) 2^kmissing1 3 17 171 2745 64771 2119329 92108379 5143290377 359335100979 30736977912561 3161546060955787
RevPolyCol3 k=0..n T(n, k) 3^kmissing1 4 30 410 9206 310674 14765830 941959042 77740110774 8063809789778 1027140312900326
RevPolyDiag k=0..n T(n, k) n^kmissing1 2 17 410 23975 2886388 624621997 220217368214 117861044130659 90851560946785640
 << TableSourceSimilarsIndex >> 

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.