A350282 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1/x^k)^n.

1, 0, 4, 62, 4658, 0, 2319512420, 14225426190522, 361926393013029354, 0, 16231015449888734994721650504, 28330316118212024049511095643949434, 200866780133770636272812495083578779133456, 0

Offset: 0

Author

Seiichi Manyama, Dec 23 2021

Keywords

• nonn

Comments

a(n) is the coefficient of x^(n^2 * (n+1)/2) in Product_{k=0..n} (1 + x^(2*k))^n.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A063865, A047653, A124995, A124996.

Cf. A350283.

Programs

PARI

a(n) = polcoef(prod(k=1, n, x^k+1/x^k)^n, 0);

PARI

a(n) = polcoef(prod(k=1, n, 1+x^(2*k))^n, n^2*(n+1)/2);

Formula

a(4*n+1) = 0.