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A245912 Number of pairs of endofunctions f, g on [n] satisfying f(g^3(i)) = f(i) for all i in [n]. 2
1, 1, 10, 207, 6856, 302345, 17812656, 1384059775, 131612023936, 14986421437329, 2051598980742400, 327546779949753551, 59790068922261980160, 12505503377433451819993, 2956768061598853524176896, 778675046844529953944661375, 228393818322135051214683406336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

MAPLE

with(combinat):

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

b:= proc(n, i) 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, 3)*j)*b(n-i*j, i-1), 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)), j=0..n):

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

CROSSREFS

Column k=3 of A245910.

Sequence in context: A027014 A088746 A293970 * A245918 A211107 A335673

Adjacent sequences:  A245909 A245910 A245911 * A245913 A245914 A245915

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 06 2014

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)