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%I #5 Feb 18 2017 22:28:34
%S 0,1,2,10,240,29088,20943360,105529651200,4254955536384000,
%T 1544043321627770880000,5603024405522854969344000000,
%U 223654797931768113135574056960000000,107131006056993617020920990202331136000000000,667107003169139201955908457896071963607040000000000000
%N Imaginary part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).
%H Daniel Suteu, <a href="/A282567/b282567.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) ~ sin(1) * A000178(n).
%F a(0) = 0, a(n) = n!*a(n-1) + A000178(n-1)*sin(Pi/2*n).
%F Lim_{n->infinity} a(n)/G(n+2) = sin(1), where G(z) is the Barnes G-function.
%e For n = 4, a(4) = 240, which is the imaginary part of A000178(4)*(1/0! + i/1! - 1/2! - i/3! + 1/4!) = 156+240*i.
%o (PARI) a(n) = imag(prod(k=0, n, k!) * sum(k=0, n, I^k/k!));
%Y The corresponding real part is A282564.
%Y Cf. A000178, A282132.
%K nonn
%O 0,3
%A _Daniel Suteu_, Feb 18 2017
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