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 A346966 #11 Jan 23 2025 08:31:40
%S A346966 1,3,14,80,559,4599,43665,470196,5666586,75600690,1106587008,
%T A346966 17636532264,304092954138,5640892517610,112029356591862,
%U A346966 2371963759970352,53338181764577304,1269586152655203672,31891196481381667008,843109673024218773600,23400930987874505081160
%N A346966 Expansion of e.g.f. -log( 1 - log(1 - x)^2 / 2 ).
%F A346966 a(n) = |Stirling1(n,2)| + (1/n) * Sum_{k=1..n-1} binomial(n,k) * |Stirling1(n-k,2)| * k * a(k).
%F A346966 a(n) ~ (n-1)! / (1 - exp(-sqrt(2)))^n. - _Vaclav Kotesovec_, Jun 04 2022
%F A346966 a(n) = Sum_{k=1..floor(n/2)} (2*k)! * |Stirling1(n,2*k)|/(k * 2^k). - _Seiichi Manyama_, Jan 23 2025
%t A346966 nmax = 22; CoefficientList[Series[-Log[1 - Log[1 - x]^2/2], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 2] &
%t A346966 a[n_] := a[n] = Abs[StirlingS1[n, 2]] + (1/n) Sum[Binomial[n, k] Abs[StirlingS1[n - k, 2]] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 2, 22}]
%Y A346966 Cf. A000254, A003713, A346921, A346944.
%K A346966 nonn
%O A346966 2,2
%A A346966 _Ilya Gutkovskiy_, Aug 09 2021