A365846 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1+x)^4 ).

1, 7, 73, 903, 12281, 177415, 2672377, 41506823, 659972089, 10689904647, 175765581817, 2925998735367, 49219210772473, 835307328307207, 14284937032826873, 245924997499453447, 4258621314671050745, 74128819286282600455, 1296324135131612708857

Offset: 0

Author

Seiichi Manyama, Sep 20 2023

Keywords

• nonn

Crossrefs

Cf. A066357, A365754, A365847, A365848.

Programs

PARI

a(n) = sum(k=0, n, binomial(3*n+k+2, k)*binomial(4*(n+1), n-k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(4*(n+1),n-k).

a(n) = (1/(n+1)) * [x^n] ( (1+x)^4 / (1-x)^3 )^(n+1). - Seiichi Manyama, Jul 31 2025