|
|
A051262
|
|
10-factorial numbers.
|
|
5
|
|
|
1, 10, 200, 6000, 240000, 12000000, 720000000, 50400000000, 4032000000000, 362880000000000, 36288000000000000, 3991680000000000000, 479001600000000000000, 62270208000000000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
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
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 10*A035279(n) = Product_{k=1..n} 10*k, n >= 1; a(0) := 1.
a(n) = n!*10^n =: (10*n)(!^10);
E.g.f.: 1/(1-10*x).
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
Sum_{n>=0) 1/a(n) = e^(1/10).
Sum_{n>=0) (-1)^n/a(n) = e^(-1/10). (End)
|
|
MAPLE
|
with(combstruct):A:=[N, {N=Cycle(Union(Z$10))}, labeled]: seq(count(A, size=n)/10, n=0..14); # Zerinvary Lajos, Dec 05 2007
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
a(n) = A048176(n+1, 0)*(-1)^n (first column of unsigned triangle).
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|