%I #5 Feb 18 2017 22:28:25

%S 1,1,1,6,156,18720,13443840,67756953600,2732085780480000,

%T 991419288020582400000,3597660477435617162035200000,

%U 143607093745702043133526671360000000,68788027941331539080620236035063808000000000,428344480781652673551035086691251861743206400000000000

%N Real part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).

%H Daniel Suteu, <a href="/A282564/b282564.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) ~ cos(1) * A000178(n).

%F a(0) = 1, a(n) = n!*a(n-1) + A000178(n-1)*cos(Pi/2*n).

%F Lim_{n->infinity} a(n)/G(n+2) = cos(1), where G(z) is the Barnes G-function.

%e For n = 4, a(4) = 156, which is the real part of A000178(4)*(1/0! + i/1! - 1/2! - i/3! + 1/4!) = 156+240*i.

%o (PARI) a(n) = real(prod(k=0, n, k!) * sum(k=0, n, I^k/k!));

%Y The corresponding imaginary part is A282567.

%Y Cf. A000178, A281964.

%K nonn

%O 0,4

%A _Daniel Suteu_, Feb 18 2017