A174827 Hankel transform of A098278.
1, 2, 192, 4976640, 115579079884800, 6039552457237856256000000, 1499708022491968274577374576640000000000, 3321055547746756031053448740122923472047308800000000000000
Offset: 0
Programs
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Maple
A174827:=n->mul( ((k+1)*(2*k+1)*(2*k+2)*floor((2*k+3)/2))^(n-k), k=0..n): seq(A174827(n), n=0..7); # Wesley Ivan Hurt, Sep 13 2014
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Mathematica
Table[Product[((k + 1) (2 k + 1) (2 k + 2) Floor[(2 k + 3)/2])^(n - k), {k, 0, n}], {n, 0, 7}] (* Wesley Ivan Hurt, Sep 13 2014 *)
Formula
a(n) = Product{k=0..n, ((k+1)*(2*k+1)*(2*k+2)*floor((2*k+3)/2))^(n-k)}.
A000178(n) divides a(n). - Peter Luschny, Sep 14 2014
a(n) ~ 2^(n*(n+3) + 41/24) * n^(2*n^2 + 7*n/2 + 31/24) * Pi^(3*(n+1)/2) / (A^(5/2) * exp(3*n^2 + 7*n/2 - 5/24)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019