A370187 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^3)^2 )^n.

1, 4, 28, 226, 1940, 17214, 155914, 1432106, 13289076, 124276528, 1169346298, 11057293526, 104986087178, 1000248093420, 9557756114130, 91559051752596, 879027678226452, 8455595252761536, 81476137225450096, 786286875175380088, 7598503022428758570

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(4*n-k,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+x^3)^2) ). See A369485.

Prog

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

Crossrefs

Cf. A370185, A370186.

Cf. A369485.

Sequence in context: A368234 A192620 A180708 * A191094 A220876 A152599

Adjacent sequences: A370184 A370185 A370186 * A370188 A370189 A370190

Keyword

nonn

Author

Seiichi Manyama, Feb 11 2024

Status

approved