A051262 - OEIS

%I #37 Aug 12 2024 01:28:10

%S 1,10,200,6000,240000,12000000,720000000,50400000000,4032000000000,

%T 362880000000000,36288000000000000,3991680000000000000,

%U 479001600000000000000,62270208000000000000000

%N 10-factorial numbers.

%C For n >= 1 a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_10)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

%H Vincenzo Librandi, <a href="/A051262/b051262.txt">Table of n, a(n) for n = 0..300</a>

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

%F a(n) = 10*A035279(n) = Product_{k=1..n} 10*k, n >= 1; a(0) := 1.

%F a(n) = n!*10^n =: (10*n)(!^10);

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

%F G.f.: 1/(1 - 10*x/(1 - 10*x/(1 - 20*x/(1 - 20*x/(1 - 30*x/(1 - 30*x/(1 - ...))))))), a continued fraction. - _Ilya Gutkovskiy_, May 12 2017

%F From _Amiram Eldar_, Jun 25 2020: (Start)

%F Sum_{n>=0} 1/a(n) = e^(1/10).

%F Sum_{n>=0} (-1)^n/a(n) = e^(-1/10). (End)

%p with(combstruct):A:=[N,{N=Cycle(Union(Z$10))},labeled]: seq(count(A,size=n)/10,n=0..14); # _Zerinvary Lajos_, Dec 05 2007

%t Array[#!*10^# &, 14, 0] (* _Michael De Vlieger_, Sep 04 2017 *)

%o (Magma) [10^n*Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Oct 05 2011

%Y a(n) = A048176(n+1, 0)*(-1)^n (first column of unsigned triangle).

%Y Cf. A047058, A051188, A051189, A051232, A035279.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_