A365765 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x) ).

1, 5, 39, 365, 3772, 41491, 476410, 5644477, 68493324, 846937140, 10633195119, 135185288475, 1736883987836, 22516798984946, 294169295918996, 3869084306851933, 51189853304834940, 680816769653570044, 9097058255214149068, 122064057533865334100

Offset: 0

Author

Seiichi Manyama, Sep 18 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..865

Crossrefs

Cf. A003169, A006318, A365764, A365766.

Cf. A365752.

Programs

Mathematica

CoefficientList[(1/x) *InverseSeries[Series[x*(1-x)^4/(1+x),{x,0,20}]],x] (* Stefano Spezia, May 04 2025 *)

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(5*n-k+3,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(n+1,n-k).