OFFSET
0,5
LINKS
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; page 139.
FORMULA
E.g.f.: exp(y*log(Sum_{n>=0} n! * x^n)).
EXAMPLE
Triangle T(n,k) begins:
1;
0, 1;
0, 3, 1;
0, 26, 9, 1;
0, 426, 131, 18, 1;
0, 11064, 2910, 395, 30, 1;
0, 413640, 92314, 11475, 925, 45, 1;
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.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Sep 16 2019
STATUS
approved