A246527 Number of endofunctions on [n] whose cycle lengths are divisors of 7.

1, 1, 3, 16, 125, 1296, 16807, 262864, 4829049, 102073600, 2441582891, 65201946624, 1922453391157, 62009850843136, 2171369477933775, 82007515430081536, 3322113623606686193, 143662773881554108416, 6604529623711334804179, 321608928954695680000000

Offset

0,3

Links

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

Formula

E.g.f.: exp(Sum_{d|7} (-LambertW(-x))^d/d).

Maple

with(numtheory):
egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
a:= n-> n!*coeff(series(egf(7), 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(7, i)=0, n/i, 0))))
    end:
a:= n-> add(b(j, min(7, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Crossrefs

Column k=7 of A246522.

Sequence in context: A245012 A000951 A000272 * A159594 A246525 A193242

Adjacent sequences: A246524 A246525 A246526 * A246528 A246529 A246530

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2014

Status

approved