A370215 Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3)^2 )^n.

1, 2, 6, 26, 134, 702, 3642, 18916, 99078, 523448, 2783406, 14870418, 79743002, 428987236, 2314194840, 12514276476, 67815709958, 368183248722, 2002240199040, 10904629019548, 59468066955534, 324698112501166, 1774806572174862, 9710825272099992, 53181284133726618

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(2*n,n-3*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)^2 * (1-x^3)^2 ). See A369400.

Prog

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

Crossrefs

Cf. A369400.

Sequence in context: A030951 A030876 A159667 * A326562 A030957 A030898

Adjacent sequences: A370212 A370213 A370214 * A370216 A370217 A370218

Keyword

nonn

Author

Seiichi Manyama, Feb 12 2024

Status

approved