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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

%I

%S 1,1,10,141,9592,159245,86252976,908888155,1682479423360,

%T 128805405787953,93998774487116800,1099662085349496911,

%U 44830846497021739693056,147548082727234113659293,3534565745374740945151080448,1613371163531618738559582856125

%N Number of pairs of endofunctions f, g on [n] satisfying g^n(f(i)) = f(i) for all i in [n].

%H Alois P. Heinz, <a href="/A245988/b245988.txt">Table of n, a(n) for n = 0..100</a>

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

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

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

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

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

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

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

%p `if`(t=0, [][], m/t))))

%p end; forget(g);

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

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

%p end:

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

%Y Main diagonal of A245980.

%Y Cf. A245911.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 08 2014

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Last modified March 31 16:44 EDT 2020. Contains 333151 sequences. (Running on oeis4.)