cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

1, 1, 1, 6, 156, 18720, 13443840, 67756953600, 2732085780480000, 991419288020582400000, 3597660477435617162035200000, 143607093745702043133526671360000000, 68788027941331539080620236035063808000000000, 428344480781652673551035086691251861743206400000000000
Offset: 0

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Author

Daniel Suteu, Feb 18 2017

Keywords

Examples

			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.
		

Crossrefs

The corresponding imaginary part is A282567.

Programs

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

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.
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