login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I #15 Jun 12 2019 08:44:42

%S 1,1,7,66,786,11278,189391,3648711,79447316,1932031529,51960823060,

%T 1532677854679,49230269360973,1711283608441418,64026421121769925,

%U 2566049037080050383,109697901581313774979,4983343674745936406410

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

%H Foissy, L. <a href="https://doi.org/10.1016/j.aim.2013.03.007">Plane posets, special posets, and permutations</a>, Adv. Math. 240, 24-60 (2013).

%H J.-C. Novelli and J.-Y. Thibon, <a href="http://arXiv.org/abs/math.CO/0511200">Hopf algebras and dendriform structures arising from parking functions</a>, arXiv:math/0511200 [math.CO], 2005.

%F G.f.: (f(t)-1)/(f(t)^2) where f(t) = 1 + sum ( (n+1)^(n-1)*t^n, n >=1)

%p 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;

%t terms = 18; f[t_] = 1 + Sum[(n + 1)^(n - 1)*t^n, {n, 1, terms}];

%t CoefficientList[(f[t] - 1)/f[t]^2 + O[t]^(terms + 1), t] // Rest (* _Jean-François Alcover_, Nov 26 2017 *)

%o (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

%K nonn

%O 1,3

%A Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)