A370186 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^3)^2 )^n.

1, 3, 15, 90, 583, 3913, 26790, 185839, 1301575, 9183681, 65181645, 464858661, 3328503814, 23913207750, 172295708971, 1244484142765, 9008351053031, 65332552755149, 474622993450725, 3453219378684621, 25158758123093013, 183521479226172667, 1340195580366321837

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(3*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) * (1+x+x^3)^2) ). See A369484.

Prog

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

Crossrefs

Cf. A370185, A370187.

Cf. A369484.

Sequence in context: A205576 A173695 A255688 * A361843 A097188 A025748

Adjacent sequences: A370183 A370184 A370185 * A370187 A370188 A370189

Keyword

nonn

Author

Seiichi Manyama, Feb 11 2024

Status

approved