cp's OEIS Frontend

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

%I A103619 #16 Sep 13 2014 07:37:06
%S A103619 1,1,2,4,16,80,400,2800,22400,181440,1814400,19958400,218803200,
%T A103619 2844441600,39822182400,556972416000,8911558656000,151496497152000,
%U A103619 2579172973977600,49004286505574400,980085730111488000,19584861165821952000,430866945648082944000
%N A103619 Number of permutations of n elements admitting a cube root.
%H A103619 Alois P. Heinz, <a href="/A103619/b103619.txt">Table of n, a(n) for n = 0..250</a>
%H A103619 H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</a>, 2nd edn., Academic Press, NY, 1994, p. 149, Eq. 4.8.2.
%F A103619 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).
%p A103619 with(combinat):
%p A103619 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A103619       add(`if`(irem(j, igcd(i, 3))<>0, 0, (i-1)!^j*
%p A103619       multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)), j=0..n/i)))
%p A103619     end:
%p A103619 a:= n-> b(n$2):
%p A103619 seq(a(n), n=0..25);  # _Alois P. Heinz_, Sep 08 2014
%t A103619 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 *)
%Y A103619 Cf. A003483, A103620, A102687, A215716, A215717, A215718.
%Y A103619 Column k=3 of A247005.
%K A103619 nonn
%O A103619 0,3
%A A103619 _Vladeta Jovovic_, Feb 11 2005