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A131622 Number of cycles in all permutations of n elements with distinct cycle lengths. 1
1, 1, 8, 22, 124, 948, 6138, 50832, 468144, 5165280, 54704880, 695854080, 9016051680, 130427750880, 1994479744320, 32575206343680, 555499414471680, 10284817657927680, 196642556903116800, 3994718386866278400, 84989047758544742400, 1895851170953432985600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

E.g.f.: Sum(x^n/(n+x^n), n=1..inf) * Product(1+x^n/n, n=1..inf).

MAPLE

A131622 := proc(n) local su, i ; su := add(x^i/(i+x^i), i=1..n+1) ; for i from 1 to n do su := taylor(su*(1+x^i/i), x=0, n+1) ; od: n!*coeftayl(su, x=0, n) ; end: seq(A131622(n), n=1..30) ; # R. J. Mathar, Oct 25 2007

# second Maple program:

b:= proc(n, i) option remember; `if`(n=0, [1, 0],

      `if`(i<1, 0, `if`(i>n, 0, (p->[0, p[1]]+p)(

       b(n-i, i-1)*binomial(n, i)*(i-1)!))+b(n, i-1)))

    end:

a:= n-> b(n$2)[2]:

seq(a(n), n=1..30);  # Alois P. Heinz, May 14 2016

CROSSREFS

Cf. A000254, A007838.

Sequence in context: A033456 A264631 A026593 * A217275 A183308 A117613

Adjacent sequences:  A131619 A131620 A131621 * A131623 A131624 A131625

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 02 2007

EXTENSIONS

More terms from R. J. Mathar, Oct 25 2007

STATUS

approved

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)