OFFSET
0,3
COMMENTS
For n>0, 2*a(n) corresponds to the number of random walk labelings of the n-barbell graph. - Sela Fried, May 19 2023
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250
Sela Fried and Toufik Mansour, Further results on random walk labelings, arXiv:2305.09971 [math.CO], 2023.
FORMULA
a(n) = (2n)!/(n*(n+1)) for n>0, a(0) = 1.
a(n) = A136125(2n,n).
From Amiram Eldar, Jan 19 2021: (Start)
Sum_{n>=1} 1/a(n) = e/4 + sinh(1)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = cos(1)/4 + 3*sin(1)/4. (End)
MAPLE
a:= n-> `if`(n=0, 1, (2*n)!/(n*(n+1))):
seq(a(n), n=0..18);
MATHEMATICA
a[0] = 1; a[n_] := (2*n)!/(n*(n+1)); Array[a, 16, 0] (* Amiram Eldar, Jan 19 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 08 2018
STATUS
approved