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.

1, 7, 194, 12858, 1647384, 361351560, 125116670160, 64439768489040, 47159227114392960, 47285264408385951360, 63057420721939066617600, 109118766834521171299756800, 239996135160204867851157273600, 659114500480471292127627441484800

Offset: 1

Author

Geoffrey Critzer, Apr 13 2013

Keywords

• nonn

Links

• P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; page 139.

Crossrefs

Cf. A122949, A071605.

Programs

Mathematica

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]

PARI

N = 66;  x = 'x + O('x^N);
egf = log(sum(n=0, N, n!^2*x^n));
gf = serlaplace(egf);
v = Vec(gf)
/* Joerg Arndt, Apr 14 2013 */

Formula

E.g.f.: log(Sum_{n>=0} n!^2*x^n).

a(n) = (n!)^3 - (n-1)! * Sum_{k=1..n-1} a(k) * ((n-k)!)^2 / (k-1)!. - Ilya Gutkovskiy, Jul 10 2020