A365842 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1+x)^3 ).

1, 5, 37, 325, 3141, 32261, 345605, 3818501, 43197445, 497868805, 5825331205, 69013667845, 826213203973, 9979713945605, 121472752156677, 1488482728148997, 18346810389299205, 227319830355640325, 2829629321065267205, 35369618935665131525, 443775430273133445125

Offset: 0

Author

Seiichi Manyama, Sep 20 2023

Keywords

• nonn

Crossrefs

Cf. A007297, A365843, A365844, A365845.

Programs

PARI

a(n) = sum(k=0, n, binomial(2*n+k+1, k)*binomial(3*(n+1), n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(3*(n+1),n-k).

a(n) = (1/(n+1)) * [x^n] ( (1+x)^3 / (1-x)^2 )^(n+1). - Seiichi Manyama, Feb 17 2024