Search: id:A052182
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%I A052182
%S A052182 1,3,18,160,1875,27216,470596,9437184,215233605,5500000000,
%T A052182 155624547606,4829554409472,163086595857367,5952860799406080,
%U A052182 233543408203125000,9799832789158199296,437950726881001816329
%V A052182 1,-3,18,-160,1875,-27216,470596,-9437184,215233605,-5500000000,
%W A052182 155624547606,-4829554409472,163086595857367,-5952860799406080,
%X A052182 233543408203125000,-9799832789158199296,437950726881001816329
%N A052182 Determinant of n X n matrix whose rows are cyclic permutations of 1..n.
%C A052182 |a(n)| = number of labeled mappings from n points to themselves (endofunctions) 
               with an odd number of cycles. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 30 2006
%D A052182 P. J. Cameron and P. Cara, Independent generating sets and geometries 
               for symmetric groups, J. Algebra, Vol. 258, no. 2 (2002), 641-650.
%H A052182 T. D. Noe, <a href="b052182.txt">Table of n, a(n) for n=1..100</a>
%F A052182 a(n) = (-1)^(n-1) * n^(n-2) * (n^2 + n)/2
%F A052182 E.g.f.[A052182] = E.g.f.[A000312] * E.g.f.[A000272], so A052182(unsigned) 
               is "tree-like". E.g.f.: (T-T^2/2)/(1-T), where T=T(x) is Euler's 
               tree function (see A000169). E.g.f. for signed sequence: (W+W^2/2)/
               (1+W), where W=W(x)=-T(-x) is the Lambert W function.- Len Smiley 
               (smiley(AT)math.uaa.alaska.edu), Dec 13 2001
%e A052182 a(3) = 18 because this is the determinant of [(1,2,3), (3,1,2), (2,3,
               1) ]
%t A052182 f[n_] := Module[{a = Table[i, {i, 1, n}], m = {}, k = 0}, While[k < n, 
               m = Append[m, RotateLeft[a, k]]; k++ ]; Det[m]]; Table[ f[n], {n, 
               1, 20} ]
%o A052182 (Mupad) (1+n)^(n-1)*binomial(n+2,n)*(-1)^(n) $ n=0..16 - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 01 2007
%Y A052182 Cf. A000312, A070896, A060281, A060435.
%Y A052182 Sequence in context: A075678 A089901 A067302 this_sequence A115415 A065058 
               A032031
%Y A052182 Adjacent sequences: A052179 A052180 A052181 this_sequence A052183 A052184 
               A052185
%K A052182 easy,sign,nice
%O A052182 1,2
%A A052182 Henry M. Gunn High School Mathematical Circle (joshua.zucker(AT)stanfordalumni.org), 
               Jan 26 2000
%E A052182 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 31 2000

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