A218817 Number of rooted factorizations of n-permutations into ordered cycles.

0, 1, 6, 42, 352, 3470, 39468, 509544, 7367232, 117981792, 2073609120, 39690563616, 821945839680, 18312215714832, 436766423241120, 11104557643877760, 299811706265604096, 8566939116183215232, 258298187497129564416, 8195130059917806607104, 272936837532680503188480

Offset: 0

Author

Geoffrey Critzer, Nov 06 2012

Keywords

• nonn

Comments

Linearly arrange the cycles over all permutations of {1,2,...,n} (these are called alignments in [Flajolet and Sedgewick]) then select a root.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150
• Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 119.

Programs

Maple

b:= proc(n) b(n):= n!*`if`(n=0, 1, add(b(k)/(k!*(n-k)), k=0..n-1)) end:
a:= n-> n*b(n):
seq(a(n), n=0..20); # Alois P. Heinz, Nov 06 2012

Mathematica

nn=20;a=Log[1/(1-x)];Range[0,nn]!CoefficientList[Series[x D[1/(1-a),x] ,{x,0,nn}],x]

Formula

E.g.f.: x/( (1-x)*(1 - log(1/(1-x)))^2 ).

a(n) = n*A007840(n).