A366102 Expansion of (1/x) * Series_Reversion( x*(1+x+x^4)/(1+x) ).

1, 0, 0, 0, -1, 1, -1, 1, 4, -10, 17, -25, -1, 76, -217, 443, -490, -94, 1999, -6208, 11527, -12350, -4471, 63826, -184055, 332713, -342399, -231390, 2101215, -5790892, 10230983, -9625472, -10237792, 71714387, -190381165, 324440310, -275119412, -430340403

Offset: 0

Author

Seiichi Manyama, Sep 29 2023

Keywords

• sign

Crossrefs

Cf. A366071, A366101.

Programs

PARI

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

Formula

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