A365752
Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^4 ).
Original entry on oeis.org
1, 3, 16, 103, 735, 5592, 44452, 364815, 3067558, 26290517, 228819168, 2016953848, 17968790029, 161536295244, 1463535347928, 13349907110367, 122499957767130, 1130001670577730, 10472708110616136, 97468774074103041, 910582642690819351
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(5*n-k+3, n-k))/(n+1);
-
def A365752(n):
h = binomial(5*n + 3, n) * hypergeometric([-n, n + 1], [-5 * n - 3], -1) / (n + 1)
return simplify(h)
print([A365752(n) for n in range(21)]) # Peter Luschny, Sep 20 2023
A365856
Expansion of (1/x) * Series_Reversion( x*(1+x)^2*(1-x)^5 ).
Original entry on oeis.org
1, 3, 17, 115, 863, 6903, 57687, 497683, 4398980, 39630305, 362562226, 3359252039, 31457036708, 297247495745, 2830725974514, 27140465365203, 261768686779800, 2538061348959000, 24724191398850125, 241862002342417585, 2374978445599884762
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k+1, k)*binomial(6*n-k+4, n-k))/(n+1);
-
def A365856(n):
h = binomial(6*n + 4, n) * hypergeometric([-n, 2*n + 2], [-6 * n - 4], -1) / (n + 1)
return simplify(h)
print([A365856(n) for n in range(21)]) # Peter Luschny, Sep 20 2023
A365755
Expansion of (1/x) * Series_Reversion( x*(1-x)/(1+x)^5 ).
Original entry on oeis.org
1, 6, 52, 530, 5919, 70098, 864784, 10994490, 143042020, 1895316632, 25487708844, 346976558318, 4772478619146, 66222166440780, 925880434336320, 13030945427540170, 184467676431001644, 2624828100099166536, 37521220349342729680, 538573138719587026440
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+k, k)*binomial(5*(n+1), n-k))/(n+1);
A365751
Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^3 ).
Original entry on oeis.org
1, 2, 8, 38, 201, 1134, 6688, 40734, 254237, 1617572, 10452416, 68408626, 452530659, 3020870352, 20324167488, 137672551630, 938154745773, 6426806842566, 44234352581896, 305743015718028, 2121318029754770, 14769052147618740, 103148538125870880
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(4*n-k+2, n-k))/(n+1);
-
def A365751(n):
h = binomial(4*n + 2, n) * hypergeometric([-n, n + 1], [-4 * n - 2], -1) / (n + 1)
return simplify(h)
print([A365751(n) for n in range(23)]) # Peter Luschny, Sep 20 2023
A365879
Expansion of (1/x) * Series_Reversion( x*(1+x)^3*(1-x)^5 ).
Original entry on oeis.org
1, 2, 10, 54, 332, 2162, 14734, 103630, 746857, 5486206, 40926152, 309202686, 2361065920, 18192978966, 141280871840, 1104603758526, 8687878404289, 68692224882620, 545681467048132, 4353096328518810, 34858239962177764, 280095777427596008
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*binomial(3*n+k+2, k)*binomial(6*n-k+4, n-k))/(n+1);
-
def A365879(n):
h = binomial(6*n + 4, n) * hypergeometric([-n, 3*(n + 1)], [-6 * n - 4], -1) / (n + 1)
return simplify(h)
print([A365879(n) for n in range(22)]) # Peter Luschny, Sep 21 2023
A365766
Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x) ).
Original entry on oeis.org
1, 6, 56, 626, 7721, 101322, 1387648, 19606874, 283711805, 4183074796, 62618441024, 949174260118, 14539621490403, 224721722650224, 3500129695446816, 54882906729334378, 865664769346769005, 13725517938819785298, 218639429113140366968
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+1, k)*binomial(6*n-k+4, n-k))/(n+1);
A365880
Expansion of (1/x) * Series_Reversion( x*(1+x)^4*(1-x)^5 ).
Original entry on oeis.org
1, 1, 6, 21, 116, 566, 3176, 17501, 101391, 590756, 3519782, 21163038, 128845344, 790810400, 4894134376, 30486741869, 191068074202, 1203710067455, 7619193325238, 48430121151156, 309011352878208, 1978450305442086, 12706836843595840
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*binomial(4*n+k+3, k)*binomial(6*n-k+4, n-k))/(n+1);
-
def A365880(n):
h = binomial(6*n + 4, n) * hypergeometric([-n, 4*(n + 1)], [-6 * n - 4], -1) / (n + 1)
return simplify(h)
print([A365880(n) for n in range(23)]) # Peter Luschny, Sep 21 2023
Showing 1-7 of 7 results.