Search: id:A010790
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%I A010790
%S A010790 1,2,12,144,2880,86400,3628800,203212800,14631321600,1316818944000,
%T A010790 144850083840000,19120211066880000,2982752926433280000,
%U A010790 542861032610856960000,114000816848279961600000
%N A010790 n!*(n+1)!.
%C A010790 Let M_n be the symmetrical n X n matrix M_n(i,j)=1/min(i,j); then for 
               n>=0 det(M_n)=(-1)^(n-1)/a(n-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 27 2002
%C A010790 If n women and n men are to be seated around a circular table, with no 
               two of the same sex seated next to each other, the number of possible 
               arrangements is a(n-1). [From Ross La Haye (rlahaye(AT)new.rr.com), 
               Jan 06 2009]
%D A010790 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, pp. 63-65.
%D A010790 Kenneth H. Rosen, Editor-in-Chief, Handbook of Discrete and Combinatorial 
               Mathematics, CRC Press, 2000, page 91. [From Ross La Haye (rlahaye(AT)new.rr.com), 
               Jan 06 2009]
%H A010790 T. D. Noe, <a href="b010790.txt">Table of n, a(n) for n=0..100</a>
%H A010790 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%F A010790 Integral representation as n-th moment of a positive function on a positive 
               half axis, in Maple notation: a(n)=int(x^n*2*sqrt(x)*BesselK(1, 2*sqrt(x)), 
               x=0..infinity), n=0, 1... Hypergeometric g.f.: a(0)=1, a(n)=subs(x=0, 
               n!*diff(1/((x-1)^2), x$n)), n=1, 2... - Karol A. Penson (penson(AT)lptl.jussieu.fr), 
               Oct 23 2001
%F A010790 Sum i=0..inf 1/a(i) = BesselI(1, 2) - 1 (where 1 is order, 2 is value) 
               - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jun 10 2004
%p A010790 f := n->n!*(n+1)!;
%p A010790 seq(add((count(Permutation(k)))^2,k=0..n),n=0..14); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Oct 17 2006
%t A010790 s=1;lst={s};Do[s+=(s*=n)*n;AppendTo[lst, s], {n, 1, 4!, 1}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
%o A010790 (Other) sage: [stirling_number1(n,1)*factorial (n-2) for n in xrange(2, 
               17)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 
               2009]
%Y A010790 Cf. A004737, A000290.
%Y A010790 Second column of triangle A129065.
%Y A010790 Sequence in context: A052740 A052742 A035049 this_sequence A086928 A001927 
               A105558
%Y A010790 Adjacent sequences: A010787 A010788 A010789 this_sequence A010791 A010792 
               A010793
%K A010790 nonn,nice,easy
%O A010790 0,2
%A A010790 N. J. A. Sloane (njas(AT)research.att.com).

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