A365146 G.f. satisfies A(x) = ( 1 + x*A(x)^2 / (1 - x*A(x)) )^2.

1, 2, 11, 76, 591, 4938, 43297, 393006, 3661500, 34813530, 336447364, 3295264162, 32636826276, 326310118860, 3289090885545, 33386999310460, 341000875306393, 3501847259286514, 36136109243651145, 374513918968721080, 3896634418483676797

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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).

Prog

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

Crossrefs

Cf. A001003, A365147.

Sequence in context: A350580 A209101 A118802 * A350680 A349408 A053481

Adjacent sequences: A365143 A365144 A365145 * A365147 A365148 A365149

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved