A366057 Expansion of (1/x) * Series_Reversion( x/(1-x+x^5) ).

1, -1, 1, -1, 1, 0, -5, 20, -55, 125, -246, 406, -461, -144, 3004, -11978, 35113, -86293, 181663, -314603, 365922, 150023, -2696308, 10969573, -32970453, 82976409, -178372934, 314133884, -367436684, -179661091, 2923282216, -11972239216, 36369188841, -92517132841

Offset: 0

Author

Seiichi Manyama, Sep 27 2023

Keywords

• sign

Crossrefs

Cf. A364522, A365702, A366051.

Programs

PARI

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

Formula

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