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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 May 25 06:43 EDT 2022. Contains 354049 sequences. (Running on oeis4.)