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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

Alois P. Heinz, Table of n, a(n) for n = 1..450

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]:

seq(a(n), n=1..30);  # Alois P. Heinz, Oct 21 2015

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

Cf. A000254, A132958, A132959, A132960, A132962, A132963.

Row sums of A293211.

Sequence in context: A162972 A202832 A069724 * A278050 A070017 A054129

Adjacent sequences:  A132958 A132959 A132960 * A132962 A132963 A132964

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Sep 06 2007

EXTENSIONS

More terms from Robert G. Wilson v, Sep 13 2007

STATUS

approved

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)