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A290095 a(n) = A275725(A060126(n)); prime factorization encodings of cycle-polynomials computed for finite permutations listed in reversed colexicographic ordering.

%I A290095 #10 Aug 18 2017 09:49:39
%S A290095 2,4,18,8,8,12,150,100,54,16,16,24,54,16,90,40,36,16,16,24,40,60,16,
%T A290095 36,1470,980,882,392,392,588,750,500,162,32,32,48,162,32,270,80,108,
%U A290095 32,32,48,80,120,32,72,750,500,162,32,32,48,1050,700,378,112,112,168,450,200,162,32,32,72,200,300,32,48,108,32,162,32,270,80,108,32,378,112,630,280
%N A290095 a(n) = A275725(A060126(n)); prime factorization encodings of cycle-polynomials computed for finite permutations listed in reversed colexicographic ordering.
%C A290095 In this context "cycle-polynomials" are single-variable polynomials where the coefficients (encoded with the exponents of prime factorization of n) are equal to the lengths of cycles in the permutation listed with index n in table A055089 (A195663). See the examples.
%H A290095 Antti Karttunen, <a href="/A290095/b290095.txt">Table of n, a(n) for n = 0..40319</a>
%H A290095 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A290095 a(n) = A275725(A060126(n)).
%F A290095 Other identities:
%F A290095 A046523(a(n)) = A290096(n).
%F A290095 A056170(a(n)) = A055090(n).
%F A290095 A046660(a(n)) = A055091(n).
%F A290095 A072411(a(n)) = A055092(n).
%F A290095 A275812(a(n)) = A055093(n).
%e A290095 Consider the first eight permutations (indices 0-7) listed in A055089:
%e A290095   1 [Only the first 1-cycle explicitly listed thus a(0) = 2^1 = 2]
%e A290095   2,1 [One transposition (2-cycle) in beginning, thus a(1) = 2^2 = 4]
%e A290095   1,3,2 [One fixed element in beginning, then transposition, thus a(2) = 2^1 * 3^2 = 18]
%e A290095   3,1,2 [One 3-cycle, thus a(3) = 2^3 = 8]
%e A290095   2,3,1 [One 3-cycle, thus a(4) = 2^3 = 8]
%e A290095   3,2,1 [One transposition jumping over a fixed element, a(5) = 2^2 * 3^1 = 12]
%e A290095   1,2,4,3 [Two 1-cycles, then a 2-cycle, thus a(6) = 2^1 * 3^1 * 5^2 = 150].
%e A290095   2,1,4,3 [Two 2-cycles, not crossed, thus a(7) = 2^2 * 5^2 = 100].
%Y A290095 Cf. A055090, A055091, A055092, A055093, A060126, A290096, A290097.
%Y A290095 Cf. also A275725, A275734, A275735, A276076 and tables A055089, A195663.
%K A290095 nonn
%O A290095 0,1
%A A290095 _Antti Karttunen_, Aug 17 2017