A372410 Coefficient of x^n in the expansion of ( (1-x+x^2) / (1-x)^3 )^n.

1, 2, 12, 77, 516, 3552, 24891, 176647, 1265508, 9132530, 66288762, 483442434, 3539626635, 26002266656, 191556630375, 1414649524077, 10469628711396, 77630719516650, 576585458828844, 4288881479411395, 31945446999811266, 238233164413294792, 1778587750475510316

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(3*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) ). See A366049.

Prog

(PARI) a(n, s=2, t=1, 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. A246437, A262440.

Cf. A366049.

Sequence in context: A285489 A121680 A277478 * A372233 A081014 A223771

Adjacent sequences: A372407 A372408 A372409 * A372411 A372412 A372413

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved