A370617 Coefficient of x^n in the expansion of 1 / (1-x-x^2)^(2*n).

1, 2, 14, 98, 726, 5522, 42770, 335512, 2656998, 21195944, 170076214, 1371181110, 11098310730, 90128497032, 734008622872, 5992486341248, 49028047353670, 401885885751630, 3299812135410080, 27134786911366212, 223433635272820126, 1842041118321640390

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,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-x^2)^2 ). See A368961.

Prog

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

Crossrefs

Cf. A370618, A370619.

Cf. A368961.

Sequence in context: A322262 A109808 A304444 * A247481 A037516 A037719

Adjacent sequences: A370614 A370615 A370616 * A370618 A370619 A370620

Keyword

nonn

Author

Seiichi Manyama, Apr 30 2024

Status

approved