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A212789 Number of endofunctions on [n] with distinct cycle lengths. 2
1, 1, 3, 20, 186, 2229, 32790, 572018, 11541600, 264370473, 6776462320, 192163455384, 5972728750560, 201906797867085, 7375152706023648, 289473254317393110, 12149690892777901568, 543010240381452000273, 25746662043469525754880, 1290829803802550504743036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

E.g.f.: A(T(x)) where A(x) is e.g.f. for A007838 and T(x) is e.g.f. for A000169.

EXAMPLE

a(3)=20 because there are 27 functions f:{1,2,3}->{1,2,3} but 7 of these have at least two cycles of equal length: (1,2,3);(1,2,1);(1,2,2);(1,1,3);(1,3,3);(2,2,3)(3,2,3) where the functions are represented by their values.

MAPLE

with(combinat):

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

      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

      b(n-i*j, i-1), j=0..min(1, n/i))))

    end:

a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j$2), j=0..n):

seq(a(n), n=0..25);  # Alois P. Heinz, Aug 10 2014

MATHEMATICA

nn = 20; p = Product[1 + t^n/n, {n, 1, nn}]; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[p, {x, 0, nn}], x]

CROSSREFS

Cf. A241980.

Sequence in context: A242164 A129840 A085390 * A065980 A302581 A305460

Adjacent sequences:  A212786 A212787 A212788 * A212790 A212791 A212792

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, May 27 2012

EXTENSIONS

Terms a(8)-a(19) recomputed by Alois P. Heinz, Aug 10 2014

STATUS

approved

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Last modified July 25 19:34 EDT 2021. Contains 346291 sequences. (Running on oeis4.)