|
%I #5 Oct 29 2017 13:07:20
%S 1,2,10,160,10400,3390400,6635012800,90899675360000,
%T 9962695319131360000,9827302289744364817600000,
%U 96937502343569678741652977600000,10518214548789290471667075399621491200000,13695360582395151673134516587047571322777664000000
%N Product of first n terms of the binomial transform of the factorial.
%F a(n) ~ c * exp(n+1) * BarnesG(n+2).
%F a(n) ~ c * n^(n^2/2 + n + 5/12) * (2*Pi)^(n/2 + 1/2) / (A * exp(3*n^2/4 - 13/12))
%F where c = 0.24314714161123874545254157058990661627416712475691705561000082745...
%F and A is the Glaisher-Kinkelin constant A074962.
%t Table[Product[Sum[Binomial[m, k]*k!, {k, 0, m}], {m, 0, n}], {n, 0, 12}]
%Y Cf. A000522, A047656, A086619, A294353.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Oct 29 2017
|
