login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141316 Conjecturally, number of generators of degree n of the Hopf algebra of parking functions, regarded as a dendriform trialgebra. 3
1, 0, 5, 50, 634, 9475, 163843, 3226213, 71430404, 1759835599, 47821543220, 1422411027534, 46002758077823, 1608256429511163, 60463005173005523, 2433267830904336072, 104394054462487756061, 4757234883237958801214, 229506935072122869176226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..150

J.-C. Novelli and J.-Y. Thibon, Hopf algebras and dendriform structures arising from parking functions, Fundamenta Math. 193 (2007), 189-241.

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions, arXiv:0806.3682 [math.CO], 2008; Discrete Math. 310 (2010), no. 24, 3584-3606. See Eq. (120).

FORMULA

G.f.: (f(t)-1)/(2f(t)^2-f(t)) where f(t) = 1 + Sum_{n>=1} (n+1)^(n-1)*t^n.

a(n) ~ exp(1) * n^(n-1). - Vaclav Kotesovec, Sep 10 2014

MAPLE

f:= proc(N) 1+add((n+1)^(n-1)*t^n, n=1..N) end: g:= proc(N) taylor( (f(N)-1)/ (2*f(N)^2-f(N)), t, N+1) end: a:= proc(n) coeff(g(n), t, n) end: seq(a(n), n=1..20);

MATHEMATICA

terms = 20; f[t_] = 1 + Sum[(n + 1)^(n - 1)*t^n, {n, 1, terms}]; (1/t)* (f[t] - 1)/(2*f[t]^2 - f[t]) + O[t]^terms // CoefficientList[#, t]& (* Jean-Fran├žois Alcover, Nov 08 2017, after Vaclav Kotesovec *)

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)/(2*P^2-P); for (n=1, m, print1(polcoeff(Q, n, u), ", ")); } \\ Michel Marcus, Feb 12 2013

CROSSREFS

Cf. A122705, A122708, A185281.

Sequence in context: A234464 A047736 A185272 * A217794 A093146 A049393

Adjacent sequences:  A141313 A141314 A141315 * A141317 A141318 A141319

KEYWORD

nonn

AUTHOR

Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 00:08 EDT 2021. Contains 345403 sequences. (Running on oeis4.)