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A245911 Number of pairs of endofunctions f, g on [n] satisfying f(g^n(i)) = f(i) for all i in [n]. 3
1, 1, 12, 207, 9184, 173225, 46097856, 729481375, 454190410752, 30607186160529, 12762075858688000, 1036636706945881151, 3080713389889966460928, 145084860487902521548921, 124325137916420574135066624, 56537825009822523196823829375 (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):

T:= proc(n, j) T(n, j):= binomial(n-1, j-1)*n^(n-j) end:

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

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

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

    end:

a:= n-> add((p-> add(n^i*T(n, j)* coeff(p, x, i),

        i=0..degree(p)))(b(j$2, n)), j=0..n):

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

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, k_] := b[n, i, k] = Function[{x}, If[n == 0 || i == 1, x^n, Expand[Sum[(i - 1)!^j*multinomial[n, Join[{n - i*j}, Array[i&, j]]]/j!* x^(GCD[i, k]*j)*b[n - i*j, i - 1, k][x], {j, 0, n/i}]]]];

a[n_] := If[n == 0, 1, Sum[Binomial[n - 1, j - 1]*n^(n - j)*b[j, j, n][n], {j, 0, n}]];

a /@ Range[0, 20] (* Jean-Fran├žois Alcover, Oct 03 2019, after Alois P. Heinz *)

CROSSREFS

Main diagonal of A245910.

Cf. A245988.

Sequence in context: A151590 A297311 A217703 * A127909 A307691 A129466

Adjacent sequences:  A245908 A245909 A245910 * A245912 A245913 A245914

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 06 2014

STATUS

approved

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)