Search: id:A036740
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%I A036740
%S A036740 1,1,4,216,331776,24883200000,139314069504000000,82606411253903523840000000,
%T A036740 6984964247141514123629140377600000000,
%U A036740 109110688415571316480344899355894085582848000000000
%N A036740 (n!)^n.
%C A036740 (-1)^n*a(n) is the determinant of the n X n matrix m_{i,j}=T(n+i,j) 1<=i,
               j<=n. where T(n,k) are the signed Stirling numbers of first kind 
               A008275. Derived from methods given in Krattenthaler link. - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Sep 17 2005
%C A036740 Contribution from W. Edwin Clark (eclark(AT)math.usf.edu), Apr 09 2009: 
               (Start)
%C A036740 a(n) is also the number of binary operations on an n element set which 
               are
%C A036740 right (or left) cancellative. These are also called right (left) cancellative
%C A036740 magma or groupoids. The multiplication table of a right (left) cancellative
%C A036740 magma is an n by n matrix with entries from an n element set such that 
               the
%C A036740 elements in each column (or row) are distinct. (End)
%H A036740 Christian Krattenthaler, <a href="http://arXiv.org/abs/math/9902004">
               Advanced Determinant Calculus</a>.
%F A036740 a(n) = a(n-1)*n^n*(n-1)! = a(n-1)*A000169(n)*A000142(n) = A036740(n-1)*A000312(n)*A000142(n-1). 
               - Henry Bottomley (se16(AT)btinternet.com), Dec 06 2001
%F A036740 a(n)=prod(k=1, n, (k-1)!*k^k); a(n)=A000178(n-1)*A002109(n) - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Sep 17 2005
%p A036740 seq(mul(mul(j,j=1..n), k=1..n), n=0..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 02 2007
%p A036740 seq(mul(j^n,j=1..n), n=0..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 02 2007
%p A036740 restart:with (combinat):a:=n->mul(-stirling1(n,1), j=2..n): seq(a(n), 
               n=1..10);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 
               31 2008]
%t A036740 lst={};Do[a=n!^n;AppendTo[lst, a], {n, 0, 13}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Oct 01 2008]
%o A036740 (PARI) a(n)=n!^n
%Y A036740 A002109(n)*A000178(n-1) = (n!)^n = A036740(n) for n >= 1.
%Y A036740 Sequence in context: A042325 A091287 A055627 this_sequence A038786 A072694 
               A068210
%Y A036740 Adjacent sequences: A036737 A036738 A036739 this_sequence A036741 A036742 
               A036743
%K A036740 nonn,easy
%O A036740 0,3
%A A036740 N. J. A. Sloane (njas(AT)research.att.com).

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