A366116 Expansion of (1/x) * Series_Reversion( x*(1+x+x^3)/(1+x)^2 ).

1, 1, 1, 0, -3, -9, -15, -7, 50, 203, 429, 382, -1045, -5845, -14751, -18627, 20255, 184818, 549630, 879632, -156085, -6025489, -21267251, -40911195, -17629620, 193929269, 835617523, 1881543582, 1674869775, -5855762293, -32848801375, -85601962056, -108647926359

Offset

0,5

Links

Table of n, a(n) for n=0..32.

Formula

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

Prog

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

Crossrefs

Cf. A366117, A366118, A366119.

Cf. A366095.

Sequence in context: A270945 A355151 A370837 * A310325 A310326 A310327

Adjacent sequences: A366113 A366114 A366115 * A366117 A366118 A366119

Keyword

sign

Author

Seiichi Manyama, Sep 29 2023

Status

approved