A391514 Expansion of 1/(g^2 * (2 - g^2)), where g = 1+x*g^3 is the g.f. of A001764.

1, 0, 4, 28, 185, 1216, 8014, 53020, 352066, 2345312, 15666250, 104891172, 703676731, 4728733712, 31823846768, 214443512592, 1446624898626, 9768400008640, 66018590227746, 446521761794420, 3022156292637407, 20467200928708896, 138688582058430302, 940244117653631068

Offset

0,3

Links

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

Formula

a(n) = (1/(2*n)) * Sum_{k=1..n} k * ((-1)^k*(k+1) + Pell(k+1)) * binomial(3*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*((-1)^k*(k+1)+pell(k+1))*binomial(3*n, n-k))/(2*n));

Crossrefs

Cf. A391461, A391462, A391517.

Cf. A000129, A001764, A007226.

Sequence in context: A216211 A366810 A219405 * A001396 A155611 A218175

Adjacent sequences: A391511 A391512 A391513 * A391515 A391516 A391517

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2025

Status

approved