A370170 Coefficient of x^n in the expansion of (1+x+x^2)^(3*n).

1, 3, 21, 156, 1221, 9828, 80580, 669294, 5612805, 47419905, 402993396, 3441242544, 29502452868, 253778827695, 2189249293266, 18932541179706, 164081616775173, 1424741956592535, 12392093363519415, 107946143556797700, 941580123046540596

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(3*n-k,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)^3 ). See A365128.

Prog

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

Crossrefs

Cf. A370171, A370172.

Cf. A365128.

Sequence in context: A091171 A226560 A026333 * A205773 A192364 A286918

Adjacent sequences: A370167 A370168 A370169 * A370171 A370172 A370173

Keyword

nonn

Author

Seiichi Manyama, Feb 11 2024

Status

approved