Search: id:A054946
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%I A054946
%S A054946 1,0,2,24,544,22320,1677488,236522496,64026088576,33832910196480,
%T A054946 35262092417856512,72926863133112198144,300318571786159783496704,
%U A054946 2467430973323656141183549440,40490606137578335674252914280448
%N A054946 Number of strongly connected labeled tournaments on n nodes.
%D A054946 E. M. Wright, The number of irreducible tournaments, Glasgow Math. J., 
               11 (1970), 97-101.
%H A054946 N. J. A. Sloane, <a href="b054946.txt">Table of n, a(n) for n = 1..80</
               a> [Shortened file because terms grow rapidly: see Sloane link below 
               for additional terms]
%H A054946 V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), 
               #00.2.2.
%H A054946 N. J. A. Sloane, <a href="a054946.txt">Table of n, a(n) for n = 1..100</
               a>
%F A054946 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]
%F A054946 G.f.: 1-1/(1+f(x)) where f(x) = Sum_{m>=1} 2^(m(m-1)/2) x^m / m!.
%F A054946 Wright also gives an asymptotic expansion for a(n).
%p A054946 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:
%p A054946 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:
%Y A054946 Cf. A000568 (unlabeled tournaments), A051337 (strongly connected unlabeled 
               tournaments).
%Y A054946 Sequence in context: A133413 A012236 A138450 this_sequence A046744 A000186 
               A012113
%Y A054946 Adjacent sequences: A054943 A054944 A054945 this_sequence A054947 A054948 
               A054949
%K A054946 nonn,easy
%O A054946 1,3
%A A054946 N. J. A. Sloane (njas(AT)research.att.com), May 24 2000

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