|
| |
|
|
A054946
|
|
Number of strongly connected labeled tournaments on n nodes.
|
|
3
| |
|
|
1, 0, 2, 24, 544, 22320, 1677488, 236522496, 64026088576, 33832910196480, 35262092417856512, 72926863133112198144, 300318571786159783496704, 2467430973323656141183549440, 40490606137578335674252914280448
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| E. M. Wright, The number of irreducible tournaments, Glasgow Math. J., 11 (1970), 97-101.
|
|
|
LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 1..80 [Shortened file because terms grow rapidly: see Sloane link below for additional terms]
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
N. J. A. Sloane, Table of n, a(n) for n = 1..100
|
|
|
FORMULA
| Let F(n) = 2^(n*(n-1)/2). Then a(n) is defined by the recurrence a(1)=1, F(n) = a(n) + Sum_{s=1..n-1} binomial(n,s)*a(s)*F(n-s). [Wright]
G.f.: 1-1/(1+f(x)) where f(x) = Sum_{m>=1} 2^(m(m-1)/2) x^m / m!.
Wright also gives an asymptotic expansion for a(n).
|
|
|
MAPLE
| with(powseries): powcreate(t(n)=2^(n*(n-1)/2)/n!): s := evalpow(1-1/t): a := tpsform(s, x, 21): for n from 0 to 20 do printf(`%d, `, n!*coeff(a, x, n)) od:
f:=array(0..500); F:=array(0..500); M:=100; f[1]:=1; F[1]:=1; lprint(1, f[1]); for n from 2 to M do F[n]:=2^(n*(n-1)/2); f[n]:=F[n]-add( binomial(n, s)*f[s]*F[n-s], s=1..n-1); lprint(n, f[n]); od:
|
|
|
CROSSREFS
| Cf. A000568 (unlabeled tournaments), A051337 (strongly connected unlabeled tournaments).
Sequence in context: A186414 A187658 A138450 * A046744 A000186 A012113
Adjacent sequences: A054943 A054944 A054945 * A054947 A054948 A054949
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 24 2000
|
| |
|
|
