The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #20 Feb 13 2019 03:50:19
%S 2,0,8,96,1248,18176,295040,5294592,104269312,2239225856,52150118400,
%T 1310675066880,35390943453184,1022570290544640,31498715705147392,
%U 1030904079324413952,35736902010299351040,1308417934560279396352
%N a(n) = 2^n*A122827(n).
%H 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. 35.
%t terms = 18; f[t_] = 1 + Sum[n! t^n, {n, 1, terms+1}];
%t A122827 = CoefficientList[(f[t] - 1)/f[t]^2 + O[t]^(terms+1), t] // Rest;
%t 2^Range[terms]*A122827 (* _Jean-François Alcover_, Feb 13 2019 *)
%Y Cf. A122827.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jan 23 2012