|
|
A132961
|
|
Total number of all distinct cycle sizes in all permutations of [n].
|
|
7
|
|
|
1, 2, 9, 38, 215, 1384, 10409, 86946, 825075, 8541998, 97590779, 1205343952, 16148472977, 231416203212, 3560209750005, 58104163643054, 1008693571819919, 18477578835352366, 357476371577422955, 7258865626801695048, 154893910336866444009, 3454112338490001478772
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: 1/(1-x)*Sum_{k>0} (1-exp(-x^k/k)). Exponential convolution of A132960(n) and n!: a(n) = n!*Sum_{k=1..n} A132960(k)/k!.
|
|
MAPLE
|
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add(multinomial(n, n-i*j, i$j)/j!*(i-1)!^j*(p-> p+
[0, p[1]*`if`(j>0, 1, 0)])(b(n-i*j, i-1)), j=0..n/i)))
end:
a:= n-> b(n$2)[2]:
|
|
MATHEMATICA
|
Rest[ Range[0, 21]! CoefficientList[ Series[1/(1 - x) Sum[1 - Exp[ -x^k/k], {k, 25}], {x, 0, 21}], x]] - Robert G. Wilson v, Sep 13 2007
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|