A245913 Number of pairs of endofunctions f, g on [n] satisfying f(g^4(i)) = f(i) for all i in [n].

1, 1, 12, 249, 9184, 488745, 35463456, 3212948809, 369653885952, 52089606360081, 8863922597593600, 1752215974571247801, 402913941534323970048, 106177876504463493003001, 31939024924944619647750144, 10756222724503803551432639625, 4050020577581980281160989147136

Offset: 0

Author

Alois P. Heinz, Aug 06 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A245910.

Programs

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);