A010796 a(n) = n!*(n+1)!/2.

1, 6, 72, 1440, 43200, 1814400, 101606400, 7315660800, 658409472000, 72425041920000, 9560105533440000, 1491376463216640000, 271430516305428480000, 57000408424139980800000, 13680098021793595392000000, 3720986661927857946624000000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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 Cycle.
• Eric Weisstein's World of Mathematics, Hamiltonian Path.
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A006472, A009963, A078740, A010790.

Main diagonal of A291909.

Programs

Magma

[Factorial(n)* Factorial(n+1) / 2: n in [1..20]]; // Vincenzo Librandi, Jun 11 2013

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 *)

PARI

for(n=1,30, print1(n!*(n+1)!/2, ", ")) \\ G. C. Greubel, Feb 07 2018

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)