A365133 G.f. A(x) satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^2)^2.

1, 2, 9, 48, 284, 1792, 11816, 80446, 561186, 3990398, 28815594, 210746538, 1557834174, 11620294376, 87357498949, 661194915408, 5034368831334, 38534430714502, 296341243824737, 2288568585083816, 17741278361562738, 138006870242288796, 1076905750814353045

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

From Seiichi Manyama, Oct 10 2025: (Start)

G.f.: (1/x) * Series_Reversion( x / (1 + x / (1 - x)^2)^2 ).

G.f.: B(x)^2, where B(x) is the g.f. of A367237. (End)

Prog

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

Crossrefs

Cf. A109081, A365134.

Cf. A365120, A367237.

Sequence in context: A364734 A153390 A118341 * A171803 A368961 A100427

Adjacent sequences: A365130 A365131 A365132 * A365134 A365135 A365136

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved