A370273 Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3) )^n.

1, 2, 10, 59, 362, 2277, 14581, 94572, 619242, 4084538, 27099435, 180651913, 1209036725, 8118629365, 54671662692, 369071775684, 2496852123882, 16923762715911, 114902801532622, 781296976824693, 5319705042364587, 36265061394634215, 247497082392976415

Offset: 0

Author

Seiichi Manyama, Feb 13 2024

Keywords

• nonn

Crossrefs

Cf. A369297.

Programs

PARI

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(3*n-3*k-1,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^3) ). See A369297.