A391492 Expansion of 1/(2 - g^2)^2, where g = 1+x*g^4 is the g.f. of A002293.

1, 4, 30, 244, 2059, 17748, 155128, 1369388, 12178305, 108934676, 978981816, 8831966736, 79937157313, 725510642316, 6600571123848, 60177274396360, 549656324317101, 5028868946717652, 46078316721549944, 422773854764224048, 3883755463216046700

Offset

0,2

Links

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

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A391464.

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

Crossrefs

Cf. A000129, A002293, A391464.

Sequence in context: A300159 A213102 A052604 * A388530 A390338 A357204

Adjacent sequences: A391489 A391490 A391491 * A391493 A391494 A391495

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved