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%I #19 Aug 22 2022 09:40:07
%S 1,5,31,210,1488,10826,80111,599671,4525573,34357725,262011295,
%T 2004962487,15383479300
%N Dimensions of algebraic generators of combinatorial Hopf algebra H(Heap_2).
%H J.-P. Bultel, S. Giraudo, <a href="http://arxiv.org/abs/1406.6903">Combinatorial Hopf algebras from PROs</a>, arXiv preprint arXiv:1406.6903 [math.CO], 2014-2016. <a href="https://doi.org/10.1007/s10801-016-0677-7">[DOI]</a>
%t terms = 11;
%t c[g_, t_] := c[g, t] = Sum[c[g, n, t], {n, 0, 3 terms}];
%t c[g_, n_, t_] := c[g, n, t] = P[g, n, t] - Sum[c[g, k, t] P[g, n-k-1, t], {k, 0, n - 1}];
%t P[g_, n_, t_] := 1/F[g, n, t];
%t F[g_, n_, t_] := F[g, n, t] = If[n<=g, 1, F[g, n-1, t] - t F[g, n-g-1, t]];
%t Rest[CoefficientList[1 - 1/c[2, t] + O[t]^(terms + 1), t]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 25 2018 *)
%K nonn,more
%O 0,2
%A _N. J. A. Sloane_, Sep 21 2014
%E a(12)-a(13) from _Robert G. Wilson v_, Jul 25 2018
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