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One tenth of deca-factorial numbers.
11

%I #27 Sep 08 2022 08:44:52

%S 1,20,600,24000,1200000,72000000,5040000000,403200000000,

%T 36288000000000,3628800000000000,399168000000000000,

%U 47900160000000000000,6227020800000000000000,871782912000000000000000,130767436800000000000000000,20922789888000000000000000000

%N One tenth of deca-factorial numbers.

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

%H G. C. Greubel, <a href="/A035279/b035279.txt">Table of n, a(n) for n = 1..320</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

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

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

%F From _Amiram Eldar_, Jan 08 2022: (Start)

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

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

%p seq(10^(n-1)*n!, n=1..20); # _G. C. Greubel_, Nov 11 2019

%t Table[10^(n-1)*n!, {n,20}] (* _G. C. Greubel_, Nov 11 2019 *)

%o (PARI) vector(20, n, 10^(n-1)*n! ) \\ _G. C. Greubel_, Nov 11 2019

%o (Magma) [10^(n-1)*Factorial(n): n in [1..20]]; // _G. C. Greubel_, Nov 11 2019

%o (Sage) [10^(n-1)*factorial(n) for n in (1..20)] # _G. C. Greubel_, Nov 11 2019

%o (GAP) List([1..20], n-> 10^(n-1)*Factorial(n) ); # _G. C. Greubel_, Nov 11 2019

%Y Cf. A011557, A045757.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_