OFFSET
0,2
REFERENCES
R. P. Stanley, unpublished work.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..349
FORMULA
a(n) = (n-1)! * (b(n-1) + b(n)), where b(n) is a little Schroeder number (A001003).
a(n) ~ 2^(1/4) * (1 + sqrt(2))^(2*n) * n^(n-2) / exp(n). - Vaclav Kotesovec, May 22 2018
EXAMPLE
a(3) = 2!*(3+11) = 28. There are 16 such digraphs which are triangles with a possible loop at each vertex and 12 which consist of two 2-cycles with a common vertex and a possible loop at the other two vertices.
MAPLE
a:= proc(n) option remember; `if`(n<2, n+1,
(n-1)*(6*(2*n^2-4*n+1)*a(n-1)-(n-2)*
(n-3)*(2*n-1)*a(n-2))/((n+1)*(2*n-3)))
end:
seq(a(n), n=0..20); # Alois P. Heinz, May 21 2018
MATHEMATICA
b[n_] := Hypergeometric2F1[-n, n+1, 2, -1]/2;
a[n_] := Switch[n, 0, 1, 1, 2, _, (n-1)! (b[n-1] + b[n])];
a /@ Range[0, 20] (* Jean-François Alcover, Nov 18 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Stanley, Feb 04 2005
EXTENSIONS
a(0)=1 prepended and one typo corrected by Alois P. Heinz, May 21 2018
STATUS
approved