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A245988 Number of pairs of endofunctions f, g on [n] satisfying g^n(f(i)) = f(i) for all i in [n]. 3
1, 1, 10, 141, 9592, 159245, 86252976, 908888155, 1682479423360, 128805405787953, 93998774487116800, 1099662085349496911, 44830846497021739693056, 147548082727234113659293, 3534565745374740945151080448, 1613371163531618738559582856125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = A245980(n,n).

MAPLE

with(numtheory): with(combinat): M:=multinomial:

a:= proc(n) option remember; local l, g; l, g:= sort([divisors(n)[]]),

      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; forget(g);

      `if`(n=0, 1, add(g(j, n-j, nops(l), 0)*

      stirling2(n, j)*binomial(n, j)*j!, j=0..n))

    end:

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

CROSSREFS

Main diagonal of A245980.

Cf. A245911.

Sequence in context: A277310 A277372 A181162 * A184710 A263055 A159327

Adjacent sequences:  A245985 A245986 A245987 * A245989 A245990 A245991

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 08 2014

STATUS

approved

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Last modified February 27 09:21 EST 2020. Contains 332301 sequences. (Running on oeis4.)