A366024 Expansion of (1/x) * Series_Reversion( x*(1-x)*(1+x^5) ).

1, 1, 2, 5, 14, 41, 125, 393, 1265, 4147, 13799, 46488, 158261, 543610, 1881730, 6557818, 22990323, 81026013, 286915275, 1020294605, 3642192301, 13047053600, 46885795710, 168979132425, 610640337099, 2212116899436, 8031940264223, 29224761233788

Offset: 0

Author

Seiichi Manyama, Sep 26 2023

Keywords

• nonn

Crossrefs

Cf. A063019, A063026, A366023.

Programs

Mathematica

CoefficientList[InverseSeries[Series[x(1-x)(1+x^5),{x,0,28}],x]/x,x]  (* Stefano Spezia, Sep 26 2023 *)

PARI

a(n) = sum(k=0, n\5, (-1)^k*binomial(n+k, n)*binomial(2*n-5*k, n))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+k,n) * binomial(2*n-5*k,n).