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 A316747 #23 Feb 16 2025 08:33:56
%S A316747 1,2,26,794,44810,4050362,536119946,97759687034,23495075990090,
%T A316747 7197163489723322,2737224615568742666,1265459307754418362874,
%U A316747 698926543187678223962570,454516898016585094157146682,343753040265700944173260034186,299168865461564926143049346952314
%N A316747 Stirling transform of (2*n)!.
%H A316747 Seiichi Manyama, <a href="/A316747/b316747.txt">Table of n, a(n) for n = 0..224</a>
%H A316747 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>.
%F A316747 a(n) = Sum_{k=0..n} Stirling2(n,k) * (2*k)!.
%F A316747 a(n) ~ exp(1/8) * (2*n)!.
%F A316747 a(n) ~ sqrt(Pi) * 2^(2*n + 1) * n^(2*n + 1/2) / exp(2*n - 1/8).
%F A316747 E.g.f.: Sum_{k>=0} (2*k)! * (exp(x) - 1)^k / k!. - _Seiichi Manyama_, May 20 2022
%t A316747 Table[Sum[StirlingS2[n, k]*(2*k)!, {k, 0, n}], {n, 0, 20}]
%o A316747 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*k)!*(exp(x)-1)^k/k!))) \\ _Seiichi Manyama_, May 20 2022
%Y A316747 Cf. A000670, A052841, A064618, A316748.
%K A316747 nonn
%O A316747 0,2
%A A316747 _Vaclav Kotesovec_, Jul 12 2018