OFFSET
0,4
FORMULA
G.f. satisfies: A(x) = 1 / Sum_{n>=1} (A(x)^n + x^n/A(x)^n) * x^(n*(n-1)/2) due to the Jacobi triple product identity.
EXAMPLE
G.f.: A(x) = 1 - x + x^2 - 3*x^3 + 6*x^4 - 17*x^5 + 43*x^6 - 125*x^7 +...
such that
1/A(x) = (1+x*A(x))*(1-x/A(x))*(1-x) * (1+x^2*A(x))*(1-x^2/A(x))*(1-x^2) * (1+x^3*A(x))*(1-x^3/A(x))*(1-x^3) * (1+x^4*A(x))*(1-x^4/A(x))*(1-x^4) *...
1/A(x) = (A(x) + x/A(x)) + (A(x)^2 + x^2/A(x)^2)*x + (A(x)^3 + x^3/A(x)^3)*x^3 + (A(x)^4 + x^4/A(x)^4)*x^6 + (A(x)^5 + x^5/A(x)^5)*x^10 +...
PROG
(PARI) {a(n)=local(A=1-x); for(i=1, n, A=1/prod(m=1, n, (1+x^m/A)*(1+x^m*A)*(1-x^m)+x*O(x^n))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1-x); for(i=1, n, A=1/2*(A+1/sum(m=1, sqrtint(8*n+1), (A^m+x^m/A^m)*x^(m*(m-1)/2)+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 21, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 18 2012
STATUS
approved