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 A346975 #15 Jan 23 2025 08:31:06
%S A346975 1,6,25,80,91,-1694,-22875,-193740,-1119569,-768394,101162425,
%T A346975 1930987240,23583202371,181575384906,-306743537075,-45405986594980,
%U A346975 -1070132302146089,-16439720013909794,-145808623945689375,1048196472097011600,84226169502099763051
%N A346975 Expansion of e.g.f. log( 1 + (exp(x) - 1)^3 / 3! ).
%F A346975 a(n) = Stirling2(n,3) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,3) * k * a(k).
%F A346975 a(n) ~ -(n-1)! * 2^(n+1) * cos(n*arctan(2*arctan(3^(5/6)/(2^(2/3) + 3^(1/3))) / log(1 + 6^(1/3) + 6^(2/3)))) / (4*arctan(3^(5/6)/(2^(2/3) + 3^(1/3)))^2 + log(1 + 6^(1/3) + 6^(2/3))^2)^(n/2). - _Vaclav Kotesovec_, Aug 09 2021
%F A346975 a(n) = Sum_{k=1..floor(n/3)} (-1)^(k-1) * (3*k)! * Stirling2(n,3*k)/(k * 6^k). - _Seiichi Manyama_, Jan 23 2025
%t A346975 nmax = 23; CoefficientList[Series[Log[1 + (Exp[x] - 1)^3/3!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 3] &
%t A346975 a[n_] := a[n] = StirlingS2[n, 3] - (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 3] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 3, 23}]
%Y A346975 Cf. A000392, A327504, A346974, A346976, A346977.
%Y A346975 Cf. A346390, A346945.
%K A346975 sign
%O A346975 3,2
%A A346975 _Ilya Gutkovskiy_, Aug 09 2021