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.
%I A282564 #5 Feb 18 2017 22:28:25
%S A282564 1,1,1,6,156,18720,13443840,67756953600,2732085780480000,
%T A282564 991419288020582400000,3597660477435617162035200000,
%U A282564 143607093745702043133526671360000000,68788027941331539080620236035063808000000000,428344480781652673551035086691251861743206400000000000
%N A282564 Real part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).
%H A282564 Daniel Suteu, <a href="/A282564/b282564.txt">Table of n, a(n) for n = 0..50</a>
%F A282564 a(n) ~ cos(1) * A000178(n).
%F A282564 a(0) = 1, a(n) = n!*a(n-1) + A000178(n-1)*cos(Pi/2*n).
%F A282564 Lim_{n->infinity} a(n)/G(n+2) = cos(1), where G(z) is the Barnes G-function.
%e A282564 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 A282564 (PARI) a(n) = real(prod(k=0, n, k!) * sum(k=0, n, I^k/k!));
%Y A282564 The corresponding imaginary part is A282567.
%Y A282564 Cf. A000178, A281964.
%K A282564 nonn
%O A282564 0,4
%A A282564 _Daniel Suteu_, Feb 18 2017