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 A346955 #10 Jan 23 2025 08:30:59
%S A346955 1,15,140,1050,6951,42651,253660,1594230,12463451,134921787,
%T A346955 1806513072,25539589530,355175465191,4797717669123,63797550625676,
%U A346955 860468790181686,12275324511112971,192498455326842819,3353266112959628272,63379650000684213834
%N A346955 Expansion of e.g.f. -log( 1 - (exp(x) - 1)^5 / 5! ).
%F A346955 a(n) = Stirling2(n,5) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,5) * k * a(k).
%F A346955 a(n) ~ (n-1)! / (log(120^(1/5) + 1))^n. - _Vaclav Kotesovec_, Aug 09 2021
%F A346955 a(n) = Sum_{k=1..floor(n/5)} (5*k)! * Stirling2(n,5*k)/(k * 120^k). - _Seiichi Manyama_, Jan 23 2025
%t A346955 nmax = 24; CoefficientList[Series[-Log[1 - (Exp[x] - 1)^5/5!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 5] &
%t A346955 a[n_] := a[n] = StirlingS2[n, 5] + (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 5] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 5, 24}]
%Y A346955 Cf. A000481, A000629, A003704, A327506, A346390, A346920, A346954.
%K A346955 nonn
%O A346955 5,2
%A A346955 _Ilya Gutkovskiy_, Aug 08 2021