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Hankel transform of Genocchi medians.
2

%I #7 Nov 23 2023 13:25:20

%S 1,1,16,20736,6879707136,1426576071720960000,

%T 383375999244747512217600000000,

%U 247370021455402476126653493805056000000000000

%N Hankel transform of Genocchi medians.

%C Hankel transform of A005439 (when this starts 1,1,2,8,...).

%F a(n)=Product{k=0..n, ((k+1)^4)^(n-k)}.

%F From _Vaclav Kotesovec_, Nov 23 2023: (Start)

%F a(n) = Product_{k=0..n} k!^4.

%F a(n) ~ (2*Pi)^(2*n + 2) * n^(2*n^2 + 4*n + 5/3) / (A^4 * exp(3*n^2 + 4*n - 1/3)), where A is the Glaisher-Kinkelin constant A074962. (End)

%t Table[Product[k!^4, {k, 0, n}], {n, 0, 10}] (* _Vaclav Kotesovec_, Nov 23 2023 *)

%Y Cf. A000178.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Nov 27 2009