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

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%I A350307 #18 Dec 24 2021 11:04:18
%S A350307 1,1,37,100683,42935363305,4440604747662968975,
%T A350307 161247684066768055445081543753,
%U A350307 2819198261291991623302749353791096334609249,31233334332507494719367656927521237896029724037781845363309
%N A350307 a(n) is the constant term in the expansion of Product_{j=1..n} (Sum_{k=-j..j} x^k)^n.
%C A350307 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.
%t A350307 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 *)
%o A350307 (PARI) a(n) = polcoef(prod(j=1, n, sum(k=-j, j, x^k))^n, 0);
%o A350307 (PARI) a(n) = polcoef(prod(j=1, n, sum(k=0, 2*j, x^k))^n, n^2*(n+1)/2);
%Y A350307 Cf. A128081, A128083, A350282, A350305, A350308.
%K A350307 nonn
%O A350307 0,3
%A A350307 _Seiichi Manyama_, Dec 23 2021