0,1

Expansion of f(-q, q^2) in powers of q where f() is the Ramanujan two variable theta function.

Expansion of q^(-1/24) * eta(q) * eta(q^4) * eta(q^6)^5 / ( eta(q^2) * eta(q^3) * eta(q^12) )^2 in powers of q.

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

a(n) = b(24*n+1) where b(n) is multiplicative with b(p^(2e)) = (-1)^e if p == 3, 5 (mod 8), b(p^(2e)) = +1 if p == 1, 7 (mod 8) and b(p^(2e-1)) = b(2^e) = b(3^e) = 0 if e>0.

G.f. is a period 1 Fourier series which satisfies f(-1 / (2304 t)) = 4 (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A133988.

a(5n+3) = a(5n+4) = 0. a(25n+1) = -a(n).

G.f. Sum_{k>=0} a(k) x^(24k+1) = Sum_{k} (-1)^[k/2] x^(6k+1)^2.

q - q^25 + q^49 - q^121 - q^169 + q^289 - q^361 + q^529 + q^625 + ...

(PARI) {a(n) = (-1)^n * issquare( 24*n+1) }

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

(-1)^n * A080995(n) = a(n).

Sequence in context: A010815 A080995 A121373 this_sequence A143062 A074910 A115356

Adjacent sequences: A133982 A133983 A133984 this_sequence A133986 A133987 A133988

sign

Michael Somos, Oct 01 2007, Oct 04 2007