A365752 Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^4 ).

1, 3, 16, 103, 735, 5592, 44452, 364815, 3067558, 26290517, 228819168, 2016953848, 17968790029, 161536295244, 1463535347928, 13349907110367, 122499957767130, 1130001670577730, 10472708110616136, 97468774074103041, 910582642690819351

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(n+k,k) * binomial(5*n-k+3,n-k).

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,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) * (1-x)^4 )^(n+1). - Seiichi Manyama, Feb 16 2024

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(5*n-k+3, n-k))/(n+1);
(SageMath)
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

Crossrefs

Cf. A063020, A365751, A365753.

Cf. A365856, A368079.

Cf. A365754, A370105.

Sequence in context: A091637 A278429 A341320 * A207434 A074542 A366050

Adjacent sequences: A365749 A365750 A365751 * A365753 A365754 A365755

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved