0,4

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 354 Eq. (3.11)

Expansion of chi(q)/chi(q^3)^3 in powers of q where chi() is a Ramanujan theta function.

Expansion of -q^(-1/3)*c(q^2)/c(-q) in powers of q where c() is a cubic AGM analog function.

Expansion of q^(-1/3)* (eta(q^2)^2* eta(q^3)^3* eta(q^12)^3)/ (eta(q)* eta(q^4)* eta(q^6)^6) in powers of q.

Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^2)) where f(u, v)= (1-u^3)* (1-v^3)- (1+2*u*v)* (1-u*v)^3.

Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^3)) where f(u, v)= (v+v^2+v^3)- u^3*(1-2*v+4*v^2).

Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^7)) where f(u, v)= (u-v)^8 -u*(1-u^3)* (1+8*u^3)* v*(1-v^3)* (1+8*v^3).

Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)= (v^2-u)* (v^2-w)- v^2*(v-u^2)* (v-w^2).

Given g.f. A(x), then B(x)=x*A(x^3) satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1, u2, u3, u6)= u6+u3-u1*u2 +u6*u3*(1-2*u1*u2).

Euler transform of period 12 sequence [ 1, -1, -2, 0, 1, 2, 1, 0, -2, -1, 1, 0, ...].

q + q^4 - 2*q^10 - 2*q^13 + q^16 + 4*q^19 + 4*q^22 - q^25 - 8*q^28 + ...

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2*eta(x^3+A)^3*eta(x^12+A)^3/eta(x+A)/eta(x^4+A)/eta(x^6+A)^6, n))}

A092848(n) = (-1)^n * a(n). Convolution inverse of A062244.

Sequence in context: A138189 A110090 A092848 this_sequence A107356 A124725 A106522

Adjacent sequences: A128108 A128109 A128110 this_sequence A128112 A128113 A128114

sign

Michael Somos, Feb 14 2007