OFFSET
0,3
COMMENTS
Compare to Ramanujan's continued fraction (A007325): R(x) = Product_{n>=0} (1 - x^(5*n+1))*(1 - x^(5*n+4)) / ( (1 - x^(5*n+2))*(1 - x^(5*n+3)) ) = 1/(1 + x/( 1 + x^2/( 1 + x^3/( 1 + x^4/ ... )))).
EXAMPLE
G.f.: A(x) = 1 - x + 2*x^2 - 3*x^3 + 5*x^4 - 9*x^5 + 17*x^6 - 35*x^7 + 78*x^8 - 180*x^9 + 424*x^10 - 1007*x^11 + 2397*x^12 - 5717*x^13 + 13671*x^14 + ...
PROG
(PARI) {a(n) = my(A=1); for(i=1, n,
A = prod(m=0, n, (1-x^(5*m+1)*A)*(1-x^(5*m+4)*A)/((1-x^(5*m+2)*A)*(1-x^(5*m+3)*A +x*O(x^n) )) ) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 16 2021
STATUS
approved