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A141319 INVERTi transform of A141318.

%I A141319 #23 Nov 06 2016 04:45:08
%S A141319 2,3,8,46,252,1558,9800,64115,428546,2921527,20220128,141746372,
%T A141319 1004278856,7180301580,51739691584,375370204876,2739615168344,
%U A141319 20100885190508,148179065429664,1096966770610372,8151826588836472,60787793832205004,454719634089674432
%N A141319 INVERTi transform of A141318.
%C A141319 Number of generators of degree n of the primitive Lie algebra of the Hopf algebra of 2-colored planar binary trees.
%H A141319 Alois P. Heinz, <a href="/A141319/b141319.txt">Table of n, a(n) for n = 1..1000</a>
%H A141319 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 A141319 with(numtheory):
%p A141319 b:= proc(n) option remember;
%p A141319       `if`(n=0, 1, add(add((2^d)*binomial(2*d-2,d-1),
%p A141319                    d=divisors(j)) *b(n-j), j=1..n)/n)
%p A141319     end:
%p A141319 a:= proc(n) option remember;
%p A141319       `if`(n<1, -1, -add(a(n-i) *b(i), i=1..n))
%p A141319     end:
%p A141319 seq(a(n), n=1..30);  # _Alois P. Heinz_, Jan 27 2012
%t A141319 b[n_] := b[n] = If[n==0, 1, Sum[Sum[2^d*Binomial[2*d-2, d-1], {d, Divisors[ j]}]*b[n-j], {j, 1, n}]/n]; a[n_] := a[n] = If[n<1, -1, -Sum[a[n-i]* b[i], {i, 1, n}]]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Feb 24 2016, after _Alois P. Heinz_ *)
%Y A141319 Cf. A025225, A141318.
%K A141319 nonn
%O A141319 1,1
%A A141319 Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008