A246525 Number of endofunctions on [n] whose cycle lengths are divisors of 5.

1, 1, 3, 16, 125, 1320, 17671, 286336, 5436153, 118144000, 2889312875, 78480441216, 2343333279157, 76274737767424, 2687742759243375, 101931212748928000, 4139544785141163761, 179235455194948829184, 8242391462093927638867, 401202300756829929472000

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

E.g.f.: exp(Sum_{d|5} (-LambertW(-x))^d/d).

Maple

with(numtheory):
egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
a:= n-> n!*coeff(series(egf(5), x, n+1), x, n):
seq(a(n), n=0..25);
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*
      (i-1)!^j, j=0..`if`(irem(5, i)=0, n/i, 0))))
    end:
a:= n-> add(b(j, min(5, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Crossrefs

Column k=5 of A246522.

Sequence in context: A000272 A246527 A159594 * A193242 A247591 A188805

Adjacent sequences: A246522 A246523 A246524 * A246526 A246527 A246528

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2014

Status

approved