A391515 Expansion of 1/(g^2 * (2 - g^2)), where g = 1+x*g^4 is the g.f. of A002293.

1, 0, 4, 36, 305, 2584, 22072, 190196, 1651949, 14446768, 127089352, 1123729680, 9980185679, 88981492088, 796060412136, 7143505005848, 64277004229445, 579775689683808, 5241104761646312, 47474085060620272, 430809602989835812, 3916002039900078304

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*(k+1) + Pell(k+1)) * 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*((-1)^k*(k+1)+pell(k+1))*binomial(4*n, n-k))/(2*n));

Crossrefs

Cf. A391464, A391465, A391518.

Cf. A000129, A002293, A052203.

Sequence in context: A361554 A222428 A279581 * A093186 A000765 A380068

Adjacent sequences: A391512 A391513 A391514 * A391516 A391517 A391518

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2025

Status

approved