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 A346978 #15 Sep 10 2023 08:39:08
%S A346978 1,1,4,26,234,2694,37812,626352,11962164,258787812,6255195168,
%T A346978 167072685240,4886611129320,155335056242040,5332298685827760,
%U A346978 196590247328769120,7747254471910795920,324986515253994589200,14458392906960271354560,679977065168639138610720
%N A346978 Expansion of e.g.f. 1 / sqrt(1 + 2 * log(1 - x)).
%H A346978 Seiichi Manyama, <a href="/A346978/b346978.txt">Table of n, a(n) for n = 0..390</a>
%F A346978 a(n) = Sum_{k=0..n} |Stirling1(n,k)| * (2*k-1)!!.
%F A346978 a(n) ~ n^n / (exp(n/2) * (exp(1/2) - 1)^(n + 1/2)). - _Vaclav Kotesovec_, Aug 09 2021
%F A346978 a(0) = 1; a(n) = Sum_{k=1..n} (2 - k/n) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Sep 09 2023
%t A346978 nmax = 19; CoefficientList[Series[1/Sqrt[1 + 2 Log[1 - x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A346978 Table[Sum[Abs[StirlingS1[n, k]] (2 k - 1)!!, {k, 0, n}], {n, 0, 19}]
%Y A346978 Cf. A001147, A007840, A088500, A305404, A320343.
%K A346978 nonn
%O A346978 0,3
%A A346978 _Ilya Gutkovskiy_, Aug 09 2021