A273997 Number of endofunctions on [n] whose cycle lengths are squares.

1, 1, 3, 16, 131, 1446, 19957, 329344, 6315129, 137942380, 3382214291, 92014156224, 2751300514987, 89701699067176, 3167429783609925, 120428877629249536, 4905431165356442993, 213120603686615692176, 9837426739843075654819, 480775495859934668704000

Offset

0,3

Links

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

Maple

b:= proc(n) option remember; local r, f, g;
      if n=0 then 1 else r, f, g:=0, 1, 3;
      while f<=n do r:= r+(f-1)!*b(n-f)*
         binomial(n-1, f-1); f, g:= f+g, g+2
      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, 3}; While[f <= n, r = r + (f - 1)!*b[n - f]*Binomial[n - 1, f - 1]; {f, g} = {f + g, g + 2}]; 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 *)

Crossrefs

Cf. A000290, A060435, A116956, A205801, A273994, A273996, A273998.

Sequence in context: A223897 A131490 A121673 * A051921 A023998 A241464

Adjacent sequences: A273994 A273995 A273996 * A273998 A273999 A274000

Keyword

nonn

Author

Alois P. Heinz, Jun 06 2016

Status

approved