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1, 2, 12, 144, 2880, 86400, 3628800, 203212800, 14631321600, 1316818944000, 144850083840000, 19120211066880000, 2982752926433280000, 542861032610856960000, 114000816848279961600000, 27360196043587190784000000, 7441973323855715893248000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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]
a(n-1) is also the number of (directed) Hamiltonian cycles in the complete bipartite graph K_{n,n} - Eric Weisstein, Jul 15 2011
a(n) is also number of ways to place k nonattacking semi-bishops on an n X n board, sum over all k>=0 (for definition see A187235) - from Vaclav Kotesovec, Dec 06 2011
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REFERENCES
| 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]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
S. Tanimoto, Parity alternating permutations and signed Eulerian numbers, Ann. Comb. 14 (2010) 355 (total number of PAPs of [2n+1].)
Index entries for sequences related to factorial numbers
Eric Weisstein's World of Mathematics, Complete Bipartite Graph
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
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FORMULA
| 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
With b(n)=A002378(n) for n>0 and b(0)=1, A010790(n) = b(n)*b(n-1)...*b(0). - Tom Copeland, Sep 21 2011
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MAPLE
| f:= n-> n!*(n+1)!: seq (f(n), n=0..30);
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MATHEMATICA
| 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]
Times@@@Partition[Range[0, 25]!, 2, 1] (* From Harvey P. Dale, Jun 17 2011 *)
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PROG
| (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]
(PARI) a(n)= n!^2*(n+1) \\ Charles R Greathouse IV, Jul 31 2011
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CROSSREFS
| Cf. A004737, A000290.
Second column of triangle A129065.
Sequence in context: A052740 A052742 A035049 * A086928 A001927 A105558
Adjacent sequences: A010787 A010788 A010789 * A010791 A010792 A010793
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Harvey P. Dale, Jun 17 2011.
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