OFFSET
0,2
COMMENTS
Compare to: 1/P(x)^3 = Sum_{n>=0} (-1)^n * (2*n+1) * x^(n*(n+1)/2), where P(x) is the partition function of A000041.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 8*x^2 + 33*x^3 + 152*x^4 + 728*x^5 + 3590*x^6 +...
where
1/A(x)^3 = 1 - 6*x + 13*x^3 + 20*x^6 - 27*x^10 - 34*x^15 + 41*x^21 + 48*x^28 - 55*x^36 - 62*x^45 + 69*x^55 +...+ (-1)^n*(1-7*n)*(-x)^(n*(n+1)/2) +...
PROG
(PARI) {a(n)=local(A); A=sum(m=0, n, (-1)^m*(1-7*m)*(-x)^(m*(m+1)/2) +x*O(x^n))^(-1/3); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 18 2015
STATUS
approved