A141313 - OEIS

A141313

Number of connected 2-colored parking functions.

2, 8, 88, 1472, 32448, 882880, 28551808, 1070280960, 45665892352, 2186865540096, 116223603417088, 6791553234501632, 432959358513586176, 29910735011660087296, 2226409203503868313600, 177664150563678920245248

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OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..16.

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions, arXiv:0806.3682 [math.CO], 2008.

FORMULA

a(n) = 2^n*A122708(n).

MAPLE

2^n*op(n, INVERTi([seq((k+1)^(k-1), k=1..n)]))

MATHEMATICA

terms = 16;

s = (1 - 1/(1 + Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^terms;

2^Range[16] * CoefficientList[s, t] (* Jean-François Alcover, Dec 14 2018 *)

CROSSREFS