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
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 11 2005
STATUS
approved