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 A124795 Number of permutations with given cycle structure, in the prime factorization order. 68
 1, 1, 1, 1, 2, 3, 6, 1, 3, 8, 24, 6, 120, 30, 20, 1, 720, 15, 5040, 20, 90, 144, 40320, 10, 40, 840, 15, 90, 362880, 120, 3628800, 1, 504, 5760, 420, 45, 39916800, 45360, 3360, 40, 479001600, 630, 6227020800, 504, 210, 403200, 87178291200, 15, 1260, 280, 25920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Number of permutations with k1 1-cycles, k2 2-cycles, ... LINKS Gheorghe Coserea, Table of n, a(n) for n = 1..3000 Eric Weisstein's World of Mathematics, Permutation cycle FORMULA For n=p1^k1*p2^k2*... where 2=p1 {b, {p, k}, c}; kk = ff[[All, 2]]; (kk.rr)!/Times @@ (kk!)/Times @@ (rr^kk)); Array[a, 100] (* Jean-François Alcover, Feb 02 2018 *) PROG (PARI) a(n) = {   my(f=factor(n), fsz=matsize(f)[1],      g=sum(k=1, fsz, primepi(f[k, 1]) * f[k, 2])!,      h=prod(k=1, fsz, primepi(f[k, 1])^f[k, 2]));   g/(prod(k=1, fsz, f[k, 2]!) * h); }; vector(51, n, a(n)) \\ Gheorghe Coserea, Feb 02 2018; edited by Max Alekseyev, Feb 05 2018 CROSSREFS Cf. A000040. Sequence in context: A275732 A200594 A319191 * A084459 A093095 A260611 Adjacent sequences:  A124792 A124793 A124794 * A124796 A124797 A124798 KEYWORD nonn AUTHOR Max Alekseyev, Nov 07 2006 STATUS approved

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Last modified October 23 12:04 EDT 2019. Contains 328345 sequences. (Running on oeis4.)