|
%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
|
