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 A308878 #7 Jun 29 2019 13:36:30
%S A308878 1,1,3,14,86,664,6136,66240,816672,11331552,174662304,2961774144,
%T A308878 54785368128,1097882522112,23693117756928,547844658441216,
%U A308878 13511950038494208,354086653712228352,9824794572366544896,287752569360558907392,8871374335098501292032
%N A308878 Expansion of e.g.f. (1 - log(1 + x))/(1 - 2*log(1 + x)).
%C A308878 Inverse Stirling transform of A002866.
%F A308878 a(0) = 1; a(n) = Sum_{k=1..n} Stirling1(n,k) * 2^(k-1) * k!.
%F A308878 a(n) ~ n! * exp(1/2) / (4 * (exp(1/2) - 1)^(n+1)). - _Vaclav Kotesovec_, Jun 29 2019
%t A308878 nmax = 20; CoefficientList[Series[(1 - Log[1 + x])/(1 - 2 Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A308878 Join[{1}, Table[Sum[StirlingS1[n, k] 2^(k - 1) k!, {k, 1, n}], {n, 1, 20}]]
%Y A308878 Cf. A002866, A008275, A011782, A050351, A088501, A306042, A308877.
%K A308878 nonn
%O A308878 0,3
%A A308878 _Ilya Gutkovskiy_, Jun 29 2019