|
|
A335088
|
|
a(n) = n! * [x^n] exp(Sum_{k=1..n, gcd(n,k) = 1} x^k / k).
|
|
3
|
|
|
1, 1, 1, 4, 9, 96, 145, 4320, 11025, 179200, 693441, 36288000, 62610625, 5748019200, 15259154625, 378002200576, 4108830350625, 334764638208000, 643373556450625, 115242726703104000, 309281197713168681, 14870534508544000000, 168541849294187630625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Number of permutations of [n] whose cycle lengths are relatively prime to n.
|
|
LINKS
|
|
|
MAPLE
|
b:= proc(n, m) option remember; `if`(n=0, 1, add(`if`(
igcd(j, m)=1, b(n-j, m), 0)*(n-1)!/(n-j)!, j=1..n))
end:
a:= n-> b(n$2):
|
|
MATHEMATICA
|
Table[n! SeriesCoefficient[Exp[Sum[Boole[GCD[n, k] == 1] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 22}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|