A282567 Imaginary part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).

0, 1, 2, 10, 240, 29088, 20943360, 105529651200, 4254955536384000, 1544043321627770880000, 5603024405522854969344000000, 223654797931768113135574056960000000, 107131006056993617020920990202331136000000000, 667107003169139201955908457896071963607040000000000000

Offset: 0

Author

Daniel Suteu, Feb 18 2017

Keywords

• nonn

Examples

			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.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 0..50

Crossrefs

The corresponding real part is A282564.

Cf. A000178, A282132.

Programs

PARI

a(n) = imag(prod(k=0, n, k!) * sum(k=0, n, I^k/k!));

Formula

a(n) ~ sin(1) * A000178(n).

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

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