A282564 Real part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).

1, 1, 1, 6, 156, 18720, 13443840, 67756953600, 2732085780480000, 991419288020582400000, 3597660477435617162035200000, 143607093745702043133526671360000000, 68788027941331539080620236035063808000000000, 428344480781652673551035086691251861743206400000000000

Offset

0,4

Links

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

Formula

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

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

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

Example

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.

Prog

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

Crossrefs

The corresponding imaginary part is A282567.

Cf. A000178, A281964.

Sequence in context: A128120 A237529 A306496 * A324231 A283728 A030449

Adjacent sequences: A282561 A282562 A282563 * A282565 A282566 A282567

Keyword

nonn

Author

Daniel Suteu, Feb 18 2017

Status

approved