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A273994
Number of endofunctions on [n] whose cycle lengths are Fibonacci numbers.
6
1, 1, 4, 27, 250, 2975, 43296, 744913, 14797036, 333393345, 8403026320, 234300271811, 7161316358616, 238108166195263, 8556626831402560, 330494399041444425, 13654219915946513296, 600870384794864432897, 28060233470995898505024, 1386000542545570348128235
OFFSET
0,3
LINKS
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 *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 06 2016
STATUS
approved