cp's OEIS Frontend

A220754 Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that the triple a,b,c generates a transitive group.

%I A220754 #23 Jul 11 2020 07:39:32
%S A220754 1,7,194,12858,1647384,361351560,125116670160,64439768489040,
%T A220754 47159227114392960,47285264408385951360,63057420721939066617600,
%U A220754 109118766834521171299756800,239996135160204867851157273600,659114500480471292127627441484800
%N A220754 Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that the triple a,b,c generates a transitive group.
%H A220754 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; page 139.
%F A220754 E.g.f.: log(Sum_{n>=0} n!^2*x^n).
%F A220754 a(n) = (n!)^3 - (n-1)! * Sum_{k=1..n-1} a(k) * ((n-k)!)^2 / (k-1)!. - _Ilya Gutkovskiy_, Jul 10 2020
%t A220754 nn=14; b=Sum[n!^3 x^n/n!,{n,0,nn}]; Drop[Range[0,nn]!CoefficientList[Series[Log[b],{x,0,nn}],x],1]
%o A220754 (PARI)
%o A220754 N = 66;  x = 'x + O('x^N);
%o A220754 egf = log(sum(n=0, N, n!^2*x^n));
%o A220754 gf = serlaplace(egf);
%o A220754 v = Vec(gf)
%o A220754 /* _Joerg Arndt_, Apr 14 2013 */
%Y A220754 Cf. A122949, A071605.
%K A220754 nonn
%O A220754 1,2
%A A220754 _Geoffrey Critzer_, Apr 13 2013