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.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved