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 A185161 #19 Sep 03 2025 10:29:53
%S A185161 1,2,7,36,283,2898,36169,524976,8659186,159736316,3257811334,
%T A185161 72797444280,1769125982092,46466434382032,1311960028913384,
%U A185161 39633438764146568,1275742281105759813,43593785716301112538,1576217593145774955007
%N A185161 G.f. = 1/(1-g(x)) where g(x) is the g.f. for A141309.
%H A185161 Jean-Christophe Novelli and Jean-Yves Thibon, <a href="http://arxiv.org/abs/0806.3682">Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions</a> (2008); arXiv:0806.3682 [math.CO], 2008; Discrete Math. 310 (2010), no. 24, 3584-3606. See Eq. 37.
%t A185161 terms = 19;
%t A185161 c[0] = 0; c[n_] := c[n] = n! - Sum[k! c[n - k], {k, 1, n - 1}];
%t A185161 s = (Product[1/(1 - x^k)^(2^k c[k]), {k, 1, terms}] + O[x]^terms - 1)/x;
%t A185161 g[x_] = ((-1/(1 + x s) + O[x]^terms) + 1);
%t A185161 CoefficientList[1/(1 - g[x]) + O[x]^terms, x] (* _Jean-François Alcover_, Feb 13 2019 *)
%Y A185161 Cf. A141309.
%Y A185161 Essentially the same as A141308.
%K A185161 nonn,changed
%O A185161 0,2
%A A185161 _N. J. A. Sloane_, Jan 23 2012