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A122827
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Number of independent generators of degree n of the algebra of Free quasi-symmetric functions (or Malvenuto-Reutenauer algebra of permutations) as a dendriform dialgebra (i.e., number of totally primitive elements).
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2
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1, 0, 1, 6, 39, 284, 2305, 20682, 203651, 2186744, 25463925, 319989030, 4320183527, 62412737460, 961264517369, 15730347890082, 272650924761195, 4991218317261808, 96248879172426557, 1950405560049871134, 41440841509597888495, 921333064567137032620, 21392807067461981820417
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OFFSET
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1,4
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COMMENTS
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a(n) = (n-2)*A003319(n-1) for n >= 2 (result of Foissy). For instance 39 = 3 * 13 and 284 = 4 * 71. - F. Chapoton, Apr 26 2023
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LINKS
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FORMULA
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G.f.: (f(t)-1)/f(t)^2, where f(t)=sum(n!*t^n,n>=0)
a(n) ~ n! * (1 - 4/n + 1/n^2 - 3/n^3 - 34/n^4 - 313/n^5 - 3189/n^6 - 36670/n^7 - 471381/n^8 - 6700559/n^9 - 104359132/n^10 - ...). - Vaclav Kotesovec, Feb 13 2019
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MATHEMATICA
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terms = 23; f[t_] = 1 + Sum[n! t^n, {n, 1, terms+1}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 23 2006
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STATUS
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approved
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