cp's OEIS Frontend

A327547 Triangular array read by rows: T(n,k) is the number of ordered pairs of n-permutations that generate a group with exactly k orbits, 0 <= k <= n, n >= 0.

%I A327547 #20 Jan 03 2021 16:55:56
%S A327547 1,0,1,0,3,1,0,26,9,1,0,426,131,18,1,0,11064,2910,395,30,1,0,413640,
%T A327547 92314,11475,925,45,1,0,20946960,3980172,438424,34125,1855,63,1,0,
%U A327547 1377648720,224782284,21632436,1550689,84840,3346,84,1,0,114078384000,16158371184,1353378284,87036012,4533249,185976,5586,108,1
%N A327547 Triangular array read by rows: T(n,k) is the number of ordered pairs of n-permutations that generate a group with exactly k orbits, 0 <= k <= n, n >= 0.
%H A327547 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; page 139.
%F A327547 E.g.f.: exp(y*log(Sum_{n>=0} n! * x^n)).
%e A327547 Triangle T(n,k) begins:
%e A327547   1;
%e A327547   0,      1;
%e A327547   0,      3,     1;
%e A327547   0,     26,     9,    1;
%e A327547   0,    426,   131,   18,    1;
%e A327547   0,  11064,  2910,  395,   30,  1;
%e A327547   0, 413640, 92314, 11475, 925, 45, 1;
%e A327547 T(3,2) = 9 because we have 3 ordered pairs (e,<(1,2)>), (<(1,2)>,e), (<(1,2)>,<(1,2)>) for each of the 3 transpositions in S_3.
%t A327547 nn = 7; Range[0, nn]! CoefficientList[Series[Exp[u Log[Sum[n!^2 z^n/n!, {n, 0, nn}]]], {z, 0, nn}], {z, u}] // Grid
%Y A327547 Cf. A122949 (column 1), A001044 (row sums), A220754.
%K A327547 nonn,tabl
%O A327547 0,5
%A A327547 _Geoffrey Critzer_, Sep 16 2019