A391494 Expansion of (g/(2 - g^2))^2, where g = 1+x*g^3 is the g.f. of A001764.

1, 6, 41, 286, 2006, 14090, 98967, 694752, 4873442, 34156834, 239195387, 1673678190, 11701765224, 81754091064, 570775136884, 3982320601808, 27767719611418, 193505396179922, 1347751048453107, 9382179055531386, 65281152942526198, 454018538186678746

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A391462.

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

Crossrefs

Cf. A054146, A391493, A391495.

Cf. A000129, A001764, A391462.

Sequence in context: A196954 A122371 A083067 * A000402 A186654 A390714

Adjacent sequences: A391491 A391492 A391493 * A391495 A391496 A391497

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved