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A245919 Number of pairs of endofunctions f, g on [n] satisfying f(g^10(i)) = f(i) for all i in [n]. 2

%I

%S 1,1,12,249,7744,401625,30080736,3034643689,371205076992,

%T 52680504366801,12762075858688000,4097222646625776921,

%U 1485034580150268715008,546325401769976582587561,203541885180568005538811904,89218786842877518275107415625

%N Number of pairs of endofunctions f, g on [n] satisfying f(g^10(i)) = f(i) for all i in [n].

%H Alois P. Heinz, <a href="/A245919/b245919.txt">Table of n, a(n) for n = 0..150</a>

%p with(combinat):

%p b:= proc(n, i) option remember; unapply(`if`(n=0 or i=1, x^n,

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

%p x^(igcd(i, 10)*j)*b(n-i*j, i-1)(x), j=0..n/i))), x)

%p end:

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

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

%Y Column k=10 of A245910.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 06 2014

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Last modified October 18 23:35 EDT 2021. Contains 348071 sequences. (Running on oeis4.)