A391518 Expansion of 1/(g * (2 - g^2)), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 8, 62, 497, 4090, 34312, 292050, 2513933, 21834954, 191047160, 1681848536, 14882776911, 132285766774, 1180375221976, 10568144644812, 94902929505157, 854518703562218, 7712688917309144, 69763997522241288, 632283139607006244, 5740790428680511272

Offset

0,3

Links

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

Formula

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

a(n) = (A391465(n) - A006632(n))/2 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+pell(k)+pell(k+1))*binomial(4*n, n-k))/(2*n));

Crossrefs

Cf. A391464, A391465, A391515.

Cf. A000129, A002293, A006632.

Sequence in context: A190975 A287815 A244831 * A331235 A053095 A356461

Adjacent sequences: A391515 A391516 A391517 * A391519 A391520 A391521

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2025

Status

approved