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 A184949 #28 Sep 21 2024 13:25:12
%S A184949 1,0,2,3,68,390,8334,98280,2321136,42895440,1167767640,29323831680,
%T A184949 926869947816,29169311371200,1064023191882000,39974978077332480,
%U A184949 1664929964612590080,72388846850592384000,3402723408460217089344,167636144501378081280000,8796533195129444799189120
%N A184949 E.g.f. satisfies A(x) = (1-x*A(x))^(-x*A(x)).
%H A184949 Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%H A184949 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A184949 a(n) = n! * sum(k=0..n, (n+1)^(k-1)*abs(stirling1(n-k,k))/(n-k)!).
%F A184949 a(n) ~ s*(1-r*s) * n^(n-1) / (sqrt(1 - r*s*(2-r*s)*(1-r*s)) * exp(n) * r^n), where r = 0.35521237986941340511033292... and s = 1.49319771092171695325266171... are roots of the system of equations s = (1-r*s)^(-r*s), r*s*(r*s+(-1+r*s)*log(1-r*s)) = 1-r*s. - _Vaclav Kotesovec_, May 03 2015
%F A184949 E.g.f.: (1/x) * Series_Reversion( x*(1 - x)^x ). - _Seiichi Manyama_, Sep 21 2024
%p A184949 with(combinat):
%p A184949 a := n-> n! * add((n+1)^(k-1)*abs(stirling1(n-k,k))/(n-k)!, k=0..n):
%p A184949 seq(a(n), n=0..20);
%t A184949 a[n_] := n! * Sum[(n+1)^(k-1)*Abs[StirlingS1[n-k, k]]/(n-k)!, {k, 0, n}]; Table [a[n], {n, 0, 20}] (* _Jean-François Alcover_, Apr 21 2015, from formula *)
%Y A184949 Cf. A371147.
%K A184949 nonn
%O A184949 0,3
%A A184949 _Vladimir Kruchinin_, Feb 03 2011
%E A184949 Edited by _Alois P. Heinz_, Feb 03 2011