A365129 G.f. A(x) satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^2)^2.

1, 2, 9, 44, 240, 1386, 8346, 51802, 329086, 2129330, 13984095, 92974510, 624568680, 4232731050, 28904102829, 198688337014, 1373763563150, 9547516671684, 66660156446189, 467342635522698, 3288691828900768, 23220922841177476, 164465227646878689

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(s*k,n-k).

From Seiichi Manyama, Oct 08 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 A367282. (End)

Prog

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

Crossrefs

Cf. A161634, A365130.

Cf. A000108, A365133.

Cf. A367282.

Sequence in context: A317134 A295809 A229189 * A371576 A246812 A365123

Adjacent sequences: A365126 A365127 A365128 * A365130 A365131 A365132

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2023

Status

approved