A365766 Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x) ).

1, 6, 56, 626, 7721, 101322, 1387648, 19606874, 283711805, 4183074796, 62618441024, 949174260118, 14539621490403, 224721722650224, 3500129695446816, 54882906729334378, 865664769346769005, 13725517938819785298, 218639429113140366968

Offset: 0

Author

Seiichi Manyama, Sep 18 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..811

Crossrefs

Cf. A003169, A006318, A365764, A365765.

Cf. A365753.

Programs

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(6*n-k+4,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(5*n+k+4,k) * binomial(n+1,n-k).