A350305 a(n) is the constant term in the expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^n.

1, 1, 13, 1437, 1884211, 24657701475, 3111336932350947, 3710920324904591897521, 41323213770479673319301068309, 4261037235228828189774620497534270303, 4045313784246510024420372971256850718016451185

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^k + x^(2*k))^n.

Links

• Robert Israel, Table of n, a(n) for n = 0..44

Crossrefs

Cf. A007576, A156181, A225602, A350282, A350306, A350307.

Programs

Maple

f:= n -> coeff(mul(x^k+1+1/x^k,k=1..n)^n,x,0):
map(f, [$0..12]); # Robert Israel, Jan 15 2023

Mathematica

a[n_] := Coefficient[Series[Product[(x^k + 1 + 1/x^k)^n, {k, 1, n}], {x, 0, 0}], x, 0]; Array[a, 11, 0] (* Amiram Eldar, Dec 24 2021 *)

PARI

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

PARI

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