OFFSET
0,3
COMMENTS
Also the number of random walk labelings of the 2 X (n-1) king's graph, for n > 1. - Sela Fried, Apr 14 2023
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..330
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 668
Sela Fried and Toufik Mansour, Graph labelings obtainable by random walks, arXiv:2304.05728 [math.CO], 2023.
FORMULA
D-finite with recurrence: a(0) = 0, a(1)=1, a(2)=2, a(n+1) = 4*(2*n-1)*a(n).
a(n) = 8^(n+1)*Gamma(n+3/2)/sqrt(Pi).
a(n) = n!*A003645(n-2), n>1. - R. J. Mathar, Oct 18 2013
G.f.: (1 + 4*x - 2F0([1,-1/2], [], 8*x))/8. - R. J. Mathar, Jan 25 2020
MAPLE
spec := [S, {B=Prod(C, C), C=Union(B, S), S=Union(B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Table[n!*2^(n-2)*CatalanNumber[n-1] +Boole[n==1]/2 +Boole[n==0]/4, {n, 0, 30}] (* G. C. Greubel, May 30 2022 *)
PROG
(SageMath) [2^(n-2)*factorial(n)*catalan_number(n-1) +bool(n==0)/8 +bool(n==1)/2 for n in (0..30)] # G. C. Greubel, May 30 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved