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

0,3

Links

Table of n, a(n) for n=0..27.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A063019, A063026, A366023.

Sequence in context: A128739 A356698 A036766 * A222589 A243870 A287968

Adjacent sequences: A366021 A366022 A366023 * A366025 A366026 A366027

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2023

Status

approved