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A341960 G.f. A(x) satisfies: A(x) = Product_{n>=0} (1-x^(5*n+1)*A(x)) * (1-x^(5*n+4)*A(x)) / ( (1-x^(5*n+2)*A(x)) * (1-x^(5*n+3)*A(x)) ).

%I A341960 #8 Mar 17 2021 11:47:39
%S A341960 1,-1,2,-3,5,-9,17,-35,78,-180,424,-1007,2397,-5717,13671,-32808,
%T A341960 79074,-191458,465654,-1137279,2788086,-6858079,16919890,-41856203,
%U A341960 103796588,-257976965,642512314,-1603329098,4008201233,-10037187453,25174707801,-63236031835,159064703284
%N A341960 G.f. A(x) satisfies: A(x) = Product_{n>=0} (1-x^(5*n+1)*A(x)) * (1-x^(5*n+4)*A(x)) / ( (1-x^(5*n+2)*A(x)) * (1-x^(5*n+3)*A(x)) ).
%C A341960 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/ ... )))).
%e A341960 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 + ...
%o A341960 (PARI) {a(n) = my(A=1); for(i=1,n,
%o A341960 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)}
%o A341960 for(n=0,30,print1(a(n),", "))
%Y A341960 Cf. A007325.
%K A341960 sign
%O A341960 0,3
%A A341960 _Paul D. Hanna_, Mar 16 2021