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 A367158 #10 Nov 10 2023 04:29:56 %S A367158 1,1,7,92,1824,48804,1649724,67492872,3243567552,179139978072, %T A367158 11181615816216,778466939121552,59811143359463952,5027200928936108064, %U A367158 458865351655379262432,45201262487568977507328,4779609140451030860102400,539990133396500652971120640 %N A367158 E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x). %F A367158 a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * |Stirling1(n,k)|. %F A367158 a(n) ~ 9 * n^(n-1) / (2^(5/2) * exp(23*n/27) * (exp(4/27) - 1)^(n - 1/2)). - _Vaclav Kotesovec_, Nov 10 2023 %t A367158 Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 10 2023 *) %o A367158 (PARI) a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*abs(stirling(n, k, 1))); %Y A367158 Cf. A367155, A367161, A367164. %Y A367158 Cf. A052803. %K A367158 nonn %O A367158 0,3 %A A367158 _Seiichi Manyama_, Nov 07 2023