A390423 Expansion of 1/(2 - g^2)^2, where g = 1+x*g^2 is the g.f. of A000108.

1, 4, 22, 120, 647, 3452, 18254, 95800, 499555, 2590636, 13370698, 68720584, 351900110, 1796100440, 9140521052, 46394675440, 234926244899, 1187013004748, 5985795977810, 30130232222248, 151411960478554, 759715027645320, 3806480101603812, 19046837847250320

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A289684.

a(n) = (1/(4*n)) * Sum_{k=1..n} k * ((k+2)*Pell(k+1) + (k+1)*Pell(k+2)) * binomial(2*n,n-k) for n > 0.

Prog

(PARI) pell(n) = ([2, 1; 1, 0]^n)[2, 1];
a(n) = if(n==0, 1, sum(k=1, n, k*((k+2)*pell(k+1)+(k+1)*pell(k+2))*binomial(2*n, n-k))/(4*n));

Crossrefs

Cf. A000108, A000129, A289684.

Sequence in context: A155596 A244900 A261193 * A025569 A382073 A098834

Adjacent sequences: A390420 A390421 A390422 * A390424 A390425 A390426

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved