A103619 Number of permutations of n elements admitting a cube root.

1, 1, 2, 4, 16, 80, 400, 2800, 22400, 181440, 1814400, 19958400, 218803200, 2844441600, 39822182400, 556972416000, 8911558656000, 151496497152000, 2579172973977600, 49004286505574400, 980085730111488000, 19584861165821952000, 430866945648082944000

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 149, Eq. 4.8.2.

Formula

E.g.f.: (1-x^3)^(1/3)/(1-x)*Product(1/3*exp(1/3*x^(3*m)/m)+2/3*exp(-1/6*x^(3*m)/m)*cos(1/6*3^(1/2)*x^(3*m)/m), m = 1 .. infinity).

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(`if`(irem(j, igcd(i, 3))<>0, 0, (i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 08 2014

Mathematica

CoefficientList[Series[(1-x^3)^(1/3)/(1-x) * Product[1/3*E^(1/3*x^(3*m)/m) + 2/3*E^(-1/6*x^(3*m)/m) * Cos[1/6*3^(1/2)*x^(3*m)/m], {m, 1, 20}], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 13 2014 *)

Crossrefs

Cf. A003483, A103620, A102687, A215716, A215717, A215718.

Column k=3 of A247005.

Sequence in context: A347631 A102736 A247007 * A027436 A025225 A115125

Adjacent sequences: A103616 A103617 A103618 * A103620 A103621 A103622

Keyword

nonn

Author

Vladeta Jovovic, Feb 11 2005

Status

approved