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 A346923 #20 May 09 2022 08:38:21 %S A346923 1,0,0,0,1,10,85,735,6839,69804,784580,9680000,130312336,1901581968, %T A346923 29895585356,503657235900,9051009737834,172807817059664, %U A346923 3493189152511608,74530548004474584,1673793045085649146,39467836062718058100,974939402596817961050,25177327470510057799550 %N A346923 Expansion of e.g.f. 1 / (1 - log(1 - x)^4 / 4!). %H A346923 Seiichi Manyama, <a href="/A346923/b346923.txt">Table of n, a(n) for n = 0..441</a> %F A346923 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * |Stirling1(k,4)| * a(n-k). %F A346923 a(n) ~ n! * 2^(-5/4) * 3^(1/4) / (exp(2^(3/4)*3^(1/4)) * (1 - exp(-2^(3/4)*3^(1/4)))^(n+1)). - _Vaclav Kotesovec_, Aug 08 2021 %F A346923 a(n) = Sum_{k=0..floor(n/4)} (4*k)! * |Stirling1(n,4*k)|/24^k. - _Seiichi Manyama_, May 06 2022 %t A346923 nmax = 23; CoefficientList[Series[1/(1 - Log[1 - x]^4/4!), {x, 0, nmax}], x] Range[0, nmax]! %t A346923 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Abs[StirlingS1[k, 4]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}] %o A346923 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-log(1-x)^4/4!))) \\ _Michel Marcus_, Aug 07 2021 %o A346923 (PARI) a(n) = sum(k=0, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/24^k); \\ _Seiichi Manyama_, May 06 2022 %Y A346923 Cf. A007840, A346921, A346922, A346924. %Y A346923 Cf. A000454, A346895, A347003, A353119. %K A346923 nonn %O A346923 0,6 %A A346923 _Ilya Gutkovskiy_, Aug 07 2021