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Search: id:A139216
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| A139216 |
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Expansion of q^(-1) * psi(-q) * phi(-q^9) / (psi(-q^3) * psi(q^6)) in power of q where phi(), psi() are Ramanujan theta functions. |
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+0
3
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| 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -3, 0, -4, 0, 0, 0, 4, 0, 5, 0, 0, 0, -7, 0, -8, 0, 0, 0, 12, 0, 14, 0, 0, 0, -17, 0, -20, 0, 0, 0, 24, 0, 28, 0, 0, 0, -36, 0, -40, 0, 0, 0, 52, 0, 56, 0, 0, 0, -71, 0, -80, 0, 0, 0, 96, 0, 109, 0, 0, 0, -133, 0, -144, 0, 0, 0, 182, 0, 198, 0, 0, 0, -240, 0, -268
(list; graph; listen)
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OFFSET
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-1,11
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FORMULA
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Expansion of eta(q) * eta(q^4) * eta(q^6)^2 * eta(q^9)^2 / (eta(q^2) * eta(q^3) * eta(q^12)^3 * eta(q^18)) in powers of q.
Euler transform of period 36 sequence [ -1, 0, 0, -1, -1, -1, -1, -1, -2, 0, -1, 1, -1, 0, 0, -1, -1, -2, -1, -1, 0, 0, -1, 1, -1, 0, -2, -1, -1, -1, -1, -1, 0, 0, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 4 g(t) where q = exp(2 pi i t) and g() is g.f. for A139214.
a(2*n) = 0 unless n=0.
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EXAMPLE
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1/q - 1 - q^3 + 2*q^9 + 2*q^11 - 3*q^15 - 4*q^17 + 4*q^21 + 5*q^23 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^2 * eta(x^9 + A)^2 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)^3 * eta(x^18 + A)), n))}
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CROSSREFS
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A139215(n) = -(-1)^n * a(n).
Sequence in context: A050948 A062590 A139215 this_sequence A092078 A067109 A030219
Adjacent sequences: A139213 A139214 A139215 this_sequence A139217 A139218 A139219
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 11 2008
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