0,3

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

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

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);

Column k=5 of A246522.

Sequence in context: A000272 A246527 A159594 * A193242 A247591 A188805

Adjacent sequences:  A246522 A246523 A246524 * A246526 A246527 A246528

nonn

Alois P. Heinz, Aug 28 2014

approved