A384576 G.f. A(x) satisfies A(x) = ( 1 + x * A(x*A(x))^(1/2) )^2.

1, 2, 3, 8, 27, 118, 609, 3602, 23866, 174186, 1383868, 11860702, 108889022, 1064691402, 11034753421, 120739899232, 1389891203976, 16781698952902, 211959646629376, 2793804347189762, 38347179124969391, 547046497259184494, 8096627908313404104

Offset

0,2

Links

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

Formula

See A384580.

G.f.: B(x)^2, where B(x) is the g.f. of A143500.

Prog

(PARI) a(n, k=2) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-2*j+k, j)/(2*n-2*j+k)*a(n-j, j)));

Crossrefs

Column k=2 of A384580.

Cf. A143500.

Sequence in context: A121401 A318895 A093858 * A080568 A091339 A006277

Adjacent sequences: A384573 A384574 A384575 * A384577 A384578 A384579

Keyword

nonn

Author

Seiichi Manyama, Jun 04 2025

Status

approved