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A245913
Number of pairs of endofunctions f, g on [n] satisfying f(g^4(i)) = f(i) for all i in [n].
2
1, 1, 12, 249, 9184, 488745, 35463456, 3212948809, 369653885952, 52089606360081, 8863922597593600, 1752215974571247801, 402913941534323970048, 106177876504463493003001, 31939024924944619647750144, 10756222724503803551432639625, 4050020577581980281160989147136
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, 4)*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=4 of A245910.
Sequence in context: A012066 A239777 A245919 * A245917 A265453 A367737
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 06 2014
STATUS
approved