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

0,3

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.

Formula

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

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

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]

Crossrefs

Sequence in context: A222062 A074017 A135887 * A368321 A052589 A074107

Adjacent sequences: A218814 A218815 A218816 * A218818 A218819 A218820

Keyword

nonn

Author

Geoffrey Critzer, Nov 06 2012

Status

approved