A035023 One ninth of 9-factorial numbers.

1, 18, 486, 17496, 787320, 42515280, 2678462640, 192849310080, 15620794116480, 1405871470483200, 139181275577836800, 15031577762406374400, 1758694598201545804800, 221595519373394771404800, 29915395115408294139648000, 4307816896618794356109312000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

E.g.f. is g.f. for A001019(n-1) (powers of nine).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..325
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A000142, A007559, A001019, A034171, A035012, A035013.

Cf. A035017, A035018, A035020, A035021, A035022, A045756.

Programs

Magma

[9^(n-1)*Factorial(n): n in [1..40]]; // G. C. Greubel, Oct 19 2022

Mathematica

With[{nn=20},Rest[CoefficientList[Series[(-1+1/(1-9*x))/9,{x,0,nn}],x] Range[ 0,nn]!]] (* Harvey P. Dale, Apr 07 2019 *)
Table[9^(n-1)*n!, {n, 40}] (* G. C. Greubel, Oct 19 2022 *)

SageMath

[9^(n-1)*factorial(n) for n in range(1,40)] # G. C. Greubel, Oct 19 2022

Formula

9*a(n) = (9*n)(!^9) = Product_{j=1..n} 9*j = 9^n*n!.

E.g.f.: (-1+1/(1-9*x))/9.

D-finite with recurrence: a(n) - 9*n*a(n-1) = 0. - R. J. Mathar, Jan 28 2020

From Amiram Eldar, Jan 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 9*(exp(1/9)-1).

Sum_{n>=1} (-1)^(n+1)/a(n) = 9*(1-exp(-1/9)). (End)

a(n) = A001019(n-1) * A000142(n). - G. C. Greubel, Oct 19 2022