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 A338044 #10 Jan 31 2022 10:16:58
%S A338044 1,2,30,1106,75870,8355602,1349011230,300225115346,88096432294110,
%T A338044 32956583516814482,15309575613991708830,8646194423981547656786,
%U A338044 5834064910665307876000350,4635347672272868599469126162,4283458291212292843946379302430
%N A338044 E.g.f.: Sum_{j>=0} 2^j * (1 - exp(-j*x))^j.
%H A338044 Seiichi Manyama, <a href="/A338044/b338044.txt">Table of n, a(n) for n = 0..221</a>
%F A338044 a(n) = Sum_{j=0..n} (-1)^(n-j) * 2^j * j^n * j! * Stirling2(n,j).
%F A338044 a(n) ~ c * d^n * n!^2 / sqrt(n), where d = 4.888902442941545347850916031937657541653741222401134656609725875258275714... and c = 0.4779849579705948535026794982366398948961135521828033628215401277586...
%t A338044 nmax = 20; CoefficientList[Series[1 + Sum[2^j*(1 - Exp[-j*x])^j, {j, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%t A338044 Table[Sum[(-1)^(n-j) * 2^j * j^n * j! * StirlingS2[n, j], {j, 0, n}], {n, 1, 20}]
%o A338044 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*2^k*k^n*k!*stirling(n, k, 2)); \\ _Seiichi Manyama_, Jan 31 2022
%Y A338044 Cf. A195005, A220181.
%K A338044 nonn
%O A338044 0,2
%A A338044 _Vaclav Kotesovec_, Oct 08 2020