OFFSET
0,2
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
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
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 30 2010
STATUS
approved