A273994 Number of endofunctions on [n] whose cycle lengths are Fibonacci numbers.

1, 1, 4, 27, 250, 2975, 43296, 744913, 14797036, 333393345, 8403026320, 234300271811, 7161316358616, 238108166195263, 8556626831402560, 330494399041444425, 13654219915946513296, 600870384794864432897, 28060233470995898505024, 1386000542545570348128235

Offset: 0

Author

Alois P. Heinz, Jun 06 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A000045, A060435, A116956, A273001, A273996, A273997, A273998, A305824.

Programs

Maple

b:= proc(n) option remember; local r, f, g;
      if n=0 then 1 else r, f, g:= $0..2;
      while f<=n do r:= r+(f-1)!*b(n-f)*
         binomial(n-1, f-1); f, g:= g, f+g
      od; r fi
    end:
a:= n-> add(b(j)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..20);

Mathematica

b[n_] := b[n] = Module[{r, f, g}, If[n == 0, 1, {r, f, g} = {0, 1, 2}; While[f <= n, r = r + (f - 1)!*b[n - f]*Binomial[n - 1, f - 1]; {f, g} = {g, f + g}]; r]];
a[0] = 1; a[n_] := Sum[b[j]*n^(n - j)*Binomial[n - 1, j - 1], {j, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 06 2018, from Maple *)