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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
OFFSET
0,3
LINKS
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: A356973 A356960 A364989 * A245918 A368441 A211107
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 06 2014
STATUS
approved