OFFSET
0,5
COMMENTS
a(n) is the number of simple labeled graphs with n nodes and n edges. - Geoffrey Critzer, Nov 02 2014
These graphs are not necessarily covering, but the covering case is A367863, unlabeled A006649, and the unlabeled version is A001434. - Gus Wiseman, Dec 22 2023
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..370
FORMULA
a(n) ~ exp(n - 2) * n^(n - 1/2) / (sqrt(Pi) * 2^(n + 1/2)). - Vaclav Kotesovec, May 19 2020
EXAMPLE
a(5) = C(C(5,2),5) = C(10,5) = 252.
MAPLE
a:= n-> binomial(binomial(n, 2), n):
seq(a(n), n=0..20);
MATHEMATICA
nn = 18; f[x_, y_] :=
Sum[(1 + y)^Binomial[n, 2] x^n/n!, {n, 1, nn}]; Table[
n! Coefficient[Series[f[x, y], {x, 0, nn}], x^n y^n], {n, 1, nn}] (* Geoffrey Critzer, Nov 02 2014 *)
Table[Length[Subsets[Subsets[Range[n], {2}], {n}]], {n, 0, 5}] (* Gus Wiseman, Dec 22 2023 *)
PROG
(Sage) [(binomial(binomial(n+2, n), n+2)) for n in range(-1, 17)] # Zerinvary Lajos, Nov 30 2009
(Magma) [0] cat [(Binomial(Binomial(n+2, n), n+2)): n in [0..20]]; // Vincenzo Librandi, Nov 03 2014
(Python)
from math import comb
def A116508(n): return comb(n*(n-1)>>1, n) # Chai Wah Wu, Jul 02 2024
KEYWORD
easy,nonn
AUTHOR
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Mar 21 2006
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Feb 02 2024
STATUS
approved