A366071 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x) ).

1, 0, 0, 1, -1, 1, 3, -8, 14, 1, -49, 144, -162, -139, 1159, -2532, 2036, 6062, -26282, 47440, -11474, -190071, 606163, -838984, -481092, 5479390, -13618658, 13030368, 28786262, -148598623, 294393355, -128639411, -1086088045, 3848604261, -5935686369, -1750697623

Offset

0,7

Links

Table of n, a(n) for n=0..35.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-2*k-1,n-3*k).

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^(n-k)*binomial(n+k, k)*binomial(n-2*k-1, n-3*k))/(n+1);

Crossrefs

Cf. A366095, A366096, A366097.

Cf. A366101, A366102.

Cf. A054514.

Sequence in context: A346054 A153891 A056402 * A305179 A106386 A000232

Adjacent sequences: A366068 A366069 A366070 * A366072 A366073 A366074

Keyword

sign

Author

Seiichi Manyama, Sep 29 2023

Status

approved