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%I #7 Dec 14 2018 07:38:39
%S 2,8,88,1472,32448,882880,28551808,1070280960,45665892352,
%T 2186865540096,116223603417088,6791553234501632,432959358513586176,
%U 29910735011660087296,2226409203503868313600,177664150563678920245248
%N Number of connected 2-colored parking functions.
%C Number of generators of degree n of the Hopf algebra of 2-colored parking functions. Also, dimensions of the graded components of the primitive Lie algebra of the same Hopf algebra.
%H J.-C. Novelli and J.-Y. Thibon, <a href="https://arxiv.org/abs/0806.3682">Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions</a>, arXiv:0806.3682 [math.CO], 2008.
%F a(n) = 2^n*A122708(n).
%p 2^n*op(n,INVERTi([seq((k+1)^(k-1), k=1..n)]))
%t terms = 16;
%t s = (1 - 1/(1 + Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^terms;
%t 2^Range[16] * CoefficientList[s, t] (* _Jean-François Alcover_, Dec 14 2018 *)
%K nonn
%O 1,1
%A Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008