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A245985 Number of pairs of endofunctions f, g on [n] satisfying g^8(f(i)) = f(i) for all i in [n]. 2
1, 1, 10, 213, 9592, 682545, 69119136, 9284636221, 1682479423360, 410336706483873, 129022118179494400, 49380786699038009061, 22121770547251791968256, 11386670423628468306437905, 6678552357682831880750669824, 4435028805132706191344837902125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

MAPLE

with(combinat): M:=multinomial:

b:= proc(n, k) local l, g; l, g:= [1, 2, 4, 8],

      proc(k, m, i, t) option remember; local d, j; d:= l[i];

        `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*

         (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,

        `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),

        `if`(t=0, [][], m/t))))

      end; g(k, n-k, nops(l), 0)

    end:

a:= n-> add(b(n, j)*stirling2(n, j)*binomial(n, j)*j!, j=0..n):

seq(a(n), n=0..20);

CROSSREFS

Column k=8 of A245980.

Sequence in context: A239771 A245987 A245981 * A309737 A211912 A213788

Adjacent sequences:  A245982 A245983 A245984 * A245986 A245987 A245988

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 08 2014

STATUS

approved

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Last modified March 28 14:24 EDT 2020. Contains 333089 sequences. (Running on oeis4.)