A391513 Expansion of 1/(g^2 * (2 - g^2)), where g = 1+x*g^2 is the g.f. of A000108.

1, 0, 4, 20, 97, 468, 2256, 10876, 52447, 252984, 1220580, 5890044, 28427026, 137211432, 662344528, 3197451224, 15436322843, 74524477168, 359803660284, 1737164916028, 8387321609038, 40495871783624, 195524970070848, 944053945629128, 4558204500847574

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

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

Crossrefs

Cf. A289684, A391459, A391516.

Cf. A000108, A000129, A115141.

Sequence in context: A151254 A232493 A240778 * A293710 A098225 A073532

Adjacent sequences: A391510 A391511 A391512 * A391514 A391515 A391516

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2025

Status

approved