A365151 G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^3 )^2.

1, 2, 15, 130, 1263, 13158, 143704, 1623766, 18824931, 222670678, 2676674916, 32604377358, 401567277063, 4992440157784, 62569729324806, 789679959184598, 10027614784648750, 128024712530277906, 1642407060905790817, 21161202394988206098

Offset: 0

Author

Seiichi Manyama, Aug 23 2023

Keywords

• nonn

Crossrefs

Cf. A365150, A365152.

Programs

PARI

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

Formula

If g.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x))^s )^t, then a(n) = Sum_{k=0..n} binomial(t*(n+k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n+k+1).