A052648 Expansion of e.g.f. 5*x/(1-x).

0, 5, 10, 30, 120, 600, 3600, 25200, 201600, 1814400, 18144000, 199584000, 2395008000, 31135104000, 435891456000, 6538371840000, 104613949440000, 1778437140480000, 32011868528640000, 608225502044160000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 595
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

Crossrefs

Cf. A000142, A052849 (k=2), A052560 (k=3), A052578 (k=4).

Programs

Maple

spec := [S,{S=Prod(Sequence(Z),Union(Z,Z,Z,Z,Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

With[{nn=20},CoefficientList[Series[(5x)/(1-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 01 2016 *)

Formula

E.g.f.: 5*x/(1-x)

Recurrence: {a(0)=0, (-1-n)*a(n)+a(n+1)=0, a(1)=5}

a(n) = 5*n!, n>0.