0,2

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

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]

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, pp. 63-65.

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]

T. D. Noe, Table of n, a(n) for n=0..100

Index entries for sequences related to factorial numbers

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

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

f := n->n!*(n+1)!;

seq(add((count(Permutation(k)))^2, k=0..n), n=0..14); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 17 2006

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]

(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]

Cf. A004737, A000290.

Second column of triangle A129065.

Sequence in context: A052740 A052742 A035049 this_sequence A086928 A001927 A105558

Adjacent sequences: A010787 A010788 A010789 this_sequence A010791 A010792 A010793

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).