A052675 Expansion of e.g.f. (1-x)/(1-5*x).

1, 4, 40, 600, 12000, 300000, 9000000, 315000000, 12600000000, 567000000000, 28350000000000, 1559250000000000, 93555000000000000, 6081075000000000000, 425675250000000000000, 31925643750000000000000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..350
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 623

Crossrefs

Cf. A000142, A005054, A052562.

Programs

Maple

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

Mathematica

Table[(4/5)*(5^n*n! + Boole[n==0]/4), {n, 0, 50}] (* G. C. Greubel, Jun 12 2022 *)
With[{nn=20},CoefficientList[Series[(1-x)/(1-5x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 31 2023 *)

SageMath

[4*factorial(n)*5^(n-1) + bool(n==0)/5 for n in (0..40)] # G. C. Greubel, Jun 12 2022

Formula

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

D-finite Recurrence: a(0)=1, a(1)=4, a(n) = 5*n*a(n-1).

a(n) = 4*5^(n-1)*n!, n>0.

a(n) = (4/5) * A052562(n).

a(n) = n!*A005054(n). - R. J. Mathar, Jun 03 2022

G.f.: (4/5)*(Hypergeometric2F0([1, 1], [], 5*x) + 1/4). - G. C. Greubel, Jun 12 2022