A035279 One tenth of deca-factorial numbers.

1, 20, 600, 24000, 1200000, 72000000, 5040000000, 403200000000, 36288000000000, 3628800000000000, 399168000000000000, 47900160000000000000, 6227020800000000000000, 871782912000000000000000, 130767436800000000000000000, 20922789888000000000000000000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

E.g.f. is g.f. for A011557(n-1) (powers of ten).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..320
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A011557, A045757.

Programs

GAP

List([1..20], n-> 10^(n-1)*Factorial(n) ); # G. C. Greubel, Nov 11 2019

Magma

[10^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Nov 11 2019

Maple

seq(10^(n-1)*n!, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[10^(n-1)*n!, {n,20}] (* G. C. Greubel, Nov 11 2019 *)

PARI

vector(20, n, 10^(n-1)*n! ) \\ G. C. Greubel, Nov 11 2019

Sage

[10^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Nov 11 2019

Formula

10*a(n) = (10*n)(!^10) = Product_{j=1..n} 10*j = 10^n*n!.

E.g.f.: (-1 + (1-10*x)^(-1))/10.

From Amiram Eldar, Jan 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 10*(exp(1/10)-1).

Sum_{n>=1} (-1)^(n+1)/a(n) = 10*(1-exp(-1/10)). (End)