-1,2

Expansion of q^(-1) * (chi(q) * chi(q^15))^2 / (chi(q^3) * chi(q^5)) in powers of q where chi() is a Ramanujan theta function.

Expansion of (eta(q^2)^4 * eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30)^4) / (eta(q) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60))^2 in powers of q.

Euler transform of period 60 sequence.

G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 pi i t).

1/q + 2 + q + q^2 + 2*q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 5*q^7 + 5*q^8 + ...

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^2 + A)^4 * eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A) * eta(x^30 + A)^4) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A))^2, n))}

Convolution inverse of A145786. A145725(n) = A058727(n) = a(n) unless n=0. A133098(n) = -(-1)^n * a(n).

Sequence in context: A161040 A131059 A133098 this_sequence A117592 A117942 A066877

Adjacent sequences: A145785 A145786 A145787 this_sequence A145789 A145790 A145791

nonn

Michael Somos, Oct 23 2008