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 A122705 Dimension of the space of totally primitive elements of degree n in the Hopf algebra of parking functions, regarded as a bidendriform algebra. 2
 1, 1, 7, 66, 786, 11278, 189391, 3648711, 79447316, 1932031529, 51960823060, 1532677854679, 49230269360973, 1711283608441418, 64026421121769925, 2566049037080050383, 109697901581313774979, 4983343674745936406410 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..18. Foissy, L.  Plane posets, special posets, and permutations, Adv. Math. 240, 24-60 (2013). J.-C. Novelli and J.-Y. Thibon, Hopf algebras and dendriform structures arising from parking functions, arXiv:math/0511200 [math.CO], 2005. FORMULA G.f.: (f(t)-1)/(f(t)^2) where f(t) = 1 + sum ( (n+1)^(n-1)*t^n, n >=1) MAPLE f:=proc(N); 1+sum((n+1)^(n-1)*t^n, n=1..N); end; g:=proc(N); taylor( (f(N)-1)/(f(N)^2), t, N+1); end; a:=proc(n); coeff(g(n), t, n); end; MATHEMATICA terms = 18; f[t_] = 1 + Sum[(n + 1)^(n - 1)*t^n, {n, 1, terms}]; CoefficientList[(f[t] - 1)/f[t]^2 + O[t]^(terms + 1), t] // Rest (* Jean-François Alcover, Nov 26 2017 *) PROG (PARI) lista(m) = {t = u + O(u^(m+1)); P = 1 + sum(n=1, m, (n+1)^(n-1)*t^n); Q = (P-1)/P^2; for (n=1, m, print1(polcoeff(Q, n, u), ", ")); } \\ Michel Marcus, Feb 12 2013 CROSSREFS Sequence in context: A297310 A065097 A300991 * A185181 A024395 A215077 Adjacent sequences: A122702 A122703 A122704 * A122706 A122707 A122708 KEYWORD nonn AUTHOR Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006 STATUS approved

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Last modified December 4 08:33 EST 2023. Contains 367558 sequences. (Running on oeis4.)