|
|
A122708
|
|
Number of connected parking functions of length n. This is the number of independent algebraic generators in degree n of the Hopf algebra of parking functions.
|
|
3
|
|
|
1, 2, 11, 92, 1014, 13795, 223061, 4180785, 89191196, 2135610879, 56749806356, 1658094051392, 52851484193553, 1825606384989019, 67944616806148325, 2710939797419417118, 115448074520257458659, 5227118335211937247488, 250749489074570030593286
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Dimension of the space of primitive elements of degree n of the Hopf algebra of parking functions.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1-1/f(t) 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; a:=proc(n); coeff(taylor(1-1/f(n), t, n+1), t, n); end;
|
|
MATHEMATICA
|
terms = 19; s = (1-1/(1+Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^terms; CoefficientList[s, t] (* Jean-François Alcover, Jul 10 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006, Oct 24 2006
|
|
STATUS
|
approved
|
|
|
|