A372411 Coefficient of x^n in the expansion of ( (1-x+x^2)^2 / (1-x)^3 )^n.

1, 1, 7, 34, 183, 1001, 5578, 31459, 179063, 1026493, 5918007, 34277728, 199309146, 1162682314, 6801575641, 39885002534, 234384591991, 1379936226605, 8137835460115, 48062073927739, 284233390132183, 1682950066882489, 9975692904121556, 59190095764321975

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2)^2 ). See A369229.

Prog

(PARI) a(n, s=2, t=2, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));

Crossrefs

Cf. A092765, A369229.

Sequence in context: A351588 A080048 A177140 * A027233 A117650 A370618

Adjacent sequences: A372408 A372409 A372410 * A372412 A372413 A372414

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved