1,3

E. M. Wright, The number of irreducible tournaments, Glasgow Math. J., 11 (1970), 97-101.

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

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).

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:

Cf. A000568 (unlabeled tournaments), A051337 (strongly connected unlabeled tournaments).

Sequence in context: A133413 A012236 A138450 this_sequence A046744 A000186 A012113

Adjacent sequences: A054943 A054944 A054945 this_sequence A054947 A054948 A054949

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), May 24 2000