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Hankel transform of A098278.
1

%I #15 Feb 24 2019 10:47:43

%S 1,2,192,4976640,115579079884800,6039552457237856256000000,

%T 1499708022491968274577374576640000000000,

%U 3321055547746756031053448740122923472047308800000000000000

%N Hankel transform of A098278.

%F a(n) = Product{k=0..n, ((k+1)*(2*k+1)*(2*k+2)*floor((2*k+3)/2))^(n-k)}.

%F A000178(n) divides a(n). - _Peter Luschny_, Sep 14 2014

%F 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

%p 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

%t 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 *)

%Y Cf. A000178, A174826.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 30 2010