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 A010796 a(n) = n!*(n+1)!/2. 8
 1, 6, 72, 1440, 43200, 1814400, 101606400, 7315660800, 658409472000, 72425041920000, 9560105533440000, 1491376463216640000, 271430516305428480000, 57000408424139980800000, 13680098021793595392000000, 3720986661927857946624000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 2 in triangle A009963. a(n) = A078740(n, 2), first column of (3, 2)-Stirling2 array. Also the number of undirected Hamiltonian paths in the complete bipartite graph K_{n,n+1}. - Eric W. Weisstein, Sep 03 2017 Also, the number of undirected Hamiltonian cycles in the complete bipartite graph K_{n+1,n+1}. - Pontus von Brömssen, Sep 06 2022 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Complete Bipartite Graph. Eric Weisstein's World of Mathematics, Hamiltonian Path. Index entries for sequences related to factorial numbers. FORMULA a(n) = 2^(n-1) * A006472(n+1). a(n) = A010790(n)/2. E.g.f.: (hypergeom([1, 2], [], x)-1)/2. a(n) = Product_{k=1..n-1} (k^2+3*k+2). - Gerry Martens, May 09 2016 E.g.f.: x*hypergeom([1, 3], [], x). - Robert Israel, May 09 2016 From Amiram Eldar, Jun 25 2022: (Start) Sum_{n>=1} 1/a(n) = 2*(BesselI(1, 2) - 1). Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(1 - BesselJ(1, 2)). (End) MATHEMATICA Table[n! (n + 1)! / 2, {n, 1, 20}] (* Vincenzo Librandi, Jun 11 2013 *) Times@@@Partition[Range[20]!, 2, 1]/2 (* Harvey P. Dale, Jul 04 2017 *) PROG (Magma) [Factorial(n)* Factorial(n+1) / 2: n in [1..20]]; // Vincenzo Librandi, Jun 11 2013 (PARI) for(n=1, 30, print1(n!*(n+1)!/2, ", ")) \\ G. C. Greubel, Feb 07 2018 CROSSREFS Cf. A006472, A009963, A078740, A010790. Main diagonal of A291909. Sequence in context: A302355 A089252 A052730 * A038095 A012242 A138446 Adjacent sequences: A010793 A010794 A010795 * A010797 A010798 A010799 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 15 03:00 EDT 2024. Contains 375931 sequences. (Running on oeis4.)