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A218817 Number of rooted factorizations of n-permutations into ordered cycles. 2
0, 1, 6, 42, 352, 3470, 39468, 509544, 7367232, 117981792, 2073609120, 39690563616, 821945839680, 18312215714832, 436766423241120, 11104557643877760, 299811706265604096, 8566939116183215232, 258298187497129564416, 8195130059917806607104, 272936837532680503188480 (list; graph; refs; listen; history; text; internal format)
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 * A052589 A074107 A187121

Adjacent sequences:  A218814 A218815 A218816 * A218818 A218819 A218820

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Nov 06 2012

STATUS

approved

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Last modified November 29 14:23 EST 2020. Contains 338769 sequences. (Running on oeis4.)