A122705 Dimension of the space of totally primitive elements of degree n in the Hopf algebra of parking functions, regarded as a bidendriform algebra.

1, 1, 7, 66, 786, 11278, 189391, 3648711, 79447316, 1932031529, 51960823060, 1532677854679, 49230269360973, 1711283608441418, 64026421121769925, 2566049037080050383, 109697901581313774979, 4983343674745936406410

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: A371780 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