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A141309 INVERTi transform of A141308. 1

%I

%S 2,3,16,158,1796,24250,372656,6429927,122956714,2581840735,

%T 59084565968,1464445686726,39101805324620,1119446453417490,

%U 34220008384633264,1112764183812405300,38362648544330997488,1397884269388233025156

%N INVERTi transform of A141308.

%C Number of generators of degree n of the (free) primitive Lie algebra of the Hopf algebra of free quasi-symmetric functions of level 2.

%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.

%p INVERTi([seq(d(n,n=1..20)]); # where d(n) is A141308

%t terms = 18;

%t c[0] = 0; c[n_] := c[n] = n! - Sum[k! c[n-k], {k, 1, n-1}];

%t s = (Product[1/(1-x^k)^(2^k c[k]), {k, 1, terms+1}] + O[x]^(terms+1)-1)/x;

%t CoefficientList[-1/(1 + x s) + O[x]^(terms+1), x] // Rest (* _Jean-Fran├žois Alcover_, Feb 13 2019 *)

%Y Cf. A003319, A141307, A141308.

%K nonn

%O 1,1

%A Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008

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Last modified January 28 01:55 EST 2022. Contains 350654 sequences. (Running on oeis4.)