cp's OEIS Frontend

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.

A141309 INVERTi transform of A141308.

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%I A141309 #11 Dec 06 2020 06:26:11
%S A141309 2,3,16,158,1796,24250,372656,6429927,122956714,2581840735,
%T A141309 59084565968,1464445686726,39101805324620,1119446453417490,
%U A141309 34220008384633264,1112764183812405300,38362648544330997488,1397884269388233025156
%N A141309 INVERTi transform of A141308.
%C A141309 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 A141309 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 A141309 INVERTi([seq(d(n,n=1..20)]); # where d(n) is A141308
%t A141309 terms = 18;
%t A141309 c[0] = 0; c[n_] := c[n] = n! - Sum[k! c[n-k], {k, 1, n-1}];
%t A141309 s = (Product[1/(1-x^k)^(2^k c[k]), {k, 1, terms+1}] + O[x]^(terms+1)-1)/x;
%t A141309 CoefficientList[-1/(1 + x s) + O[x]^(terms+1), x] // Rest (* _Jean-François Alcover_, Feb 13 2019 *)
%Y A141309 Cf. A003319, A141307, A141308.
%K A141309 nonn
%O A141309 1,1
%A A141309 Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008