|
|
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
|
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
|
|
|
FORMULA
|
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
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
|
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
|
|
|
|