A350307 a(n) is the constant term in the expansion of Product_{j=1..n} (Sum_{k=-j..j} x^k)^n.

1, 1, 37, 100683, 42935363305, 4440604747662968975, 161247684066768055445081543753, 2819198261291991623302749353791096334609249, 31233334332507494719367656927521237896029724037781845363309

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..8.

Mathematica

a[n_] := Coefficient[Series[Product[Sum[x^k, {k, -j, j}]^n, {j, 1, n}], {x, 0, 0}], x, 0]; Array[a, 9, 0] (* Amiram Eldar, Dec 24 2021 *)

Prog

(PARI) a(n) = polcoef(prod(j=1, n, sum(k=-j, j, x^k))^n, 0);
(PARI) a(n) = polcoef(prod(j=1, n, sum(k=0, 2*j, x^k))^n, n^2*(n+1)/2);

Crossrefs

Cf. A128081, A128083, A350282, A350305, A350308.

Sequence in context: A015037 A262786 A140746 * A262646 A063681 A289820

Adjacent sequences: A350304 A350305 A350306 * A350308 A350309 A350310

Keyword

nonn

Author

Seiichi Manyama, Dec 23 2021

Status

approved