0,2

Euler transform of period 8 sequence [2,-5,2,2,2,-5,2,0,...].

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 214 Entry 24(ii).

Expansion of (eta(q^2)/eta(q^4))^7(eta(q^8)/eta(q))^2 in powers of q.

G.f.: A(x)/B(x), where A(x) = Sum_{m = -infinity..infinity} x^(m^2) and B(x) = Sum_{m = -infinity..infinity} x^(2*m^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 22 2005

Expansion of phi(x)/phi(x^2) where phi() is a Ramanujan theta function.

G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=1+(1-u*v)^2-v^2 . - Michael Somos Jan 31 2006

G.f. A(x) satisfies 0=f(A(x),A(x^3)) where f(u,v)=u^4-v^4+8*u*v-6*u*v*(u^2+v^2)+4*(u*v)^3 . - Michael Somos Jan 31 2006

Expansion of sqrt(m) in powers of q where m is the multiplier for the second degree modular equation.

G.f.: Prod_{n>0} ((1-x^(8n-2))(1-x^(8n-6)))^5/((1-x^(8n-1))(1-x^(8n-3))(1-x^(8n-4))(1-x^(8n-5))(1-x^(8n-7)))^2.

(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+2*x+O(x^2); while(m<n, m*=2; A=subst(A, x, x^2); A=(1+2*sqrt((A^2-1)/4))/A); polcoeff(A, n))

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^8+A)/eta(x+A))^2* (eta(x^2+A)/eta(x^4+A))^7, n))}

Apart from signs, same as A080054, which is the main entry for this sequence.

Sequence in context: A116859 A147982 A051466 this_sequence A080054 A108494 A078578

Adjacent sequences: A080012 A080013 A080014 this_sequence A080016 A080017 A080018

sign,easy

Michael Somos, Jan 20 2003