A246526 Number of endofunctions on [n] whose cycle lengths are divisors of 6.

1, 1, 4, 27, 250, 2951, 42552, 726097, 14318908, 320511105, 8029282096, 222590246099, 6765751467576, 223748991426247, 7998566722112800, 307359039816710361, 12634664945078752528, 553260940314226017473, 25711427896197877574208, 1263904006537455579001675

Offset

0,3

Links

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

Formula

E.g.f.: exp(Sum_{d|6} (-LambertW(-x))^d/d).

Maple

with(numtheory):
egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
a:= n-> n!*coeff(series(egf(6), 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(6, i)=0, n/i, 0))))
    end:
a:= n-> add(b(j, min(6, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Crossrefs

Column k=6 of A246522.

Sequence in context: A239375 A239370 A239369 * A273994 A239378 A239376

Adjacent sequences: A246523 A246524 A246525 * A246527 A246528 A246529

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2014

Status

approved