A365856 Expansion of (1/x) * Series_Reversion( x*(1+x)^2*(1-x)^5 ).

1, 3, 17, 115, 863, 6903, 57687, 497683, 4398980, 39630305, 362562226, 3359252039, 31457036708, 297247495745, 2830725974514, 27140465365203, 261768686779800, 2538061348959000, 24724191398850125, 241862002342417585, 2374978445599884762

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(2*n+k+1,k) * binomial(6*n-k+4,n-k).

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(4*n-2*k+2,n-2*k). - Seiichi Manyama, Jan 18 2024

a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^2 * (1-x)^5 )^(n+1). - Seiichi Manyama, Feb 16 2024

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k+1, k)*binomial(6*n-k+4, n-k))/(n+1);
(SageMath)
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

Crossrefs

Cf. A365854, A365855.

Cf. A365753.

Sequence in context: A174404 A271611 A112111 * A074554 A367945 A074544

Adjacent sequences: A365853 A365854 A365855 * A365857 A365858 A365859

Keyword

nonn

Author

Seiichi Manyama, Sep 20 2023

Status

approved