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Search: id:A139032
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| A139032 |
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Expansion of 1 + c(q^6) / c(q^3) where c() is a cubic AGM function. |
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3
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| 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -1, 0, 0, 4, 0, 0, -4, 0, 0, -1, 0, 0, 8, 0, 0, -8, 0, 0, -2, 0, 0, 14, 0, 0, -14, 0, 0, -4, 0, 0, 24, 0, 0, -23, 0, 0, -6, 0, 0, 40, 0, 0, -38, 0, 0, -10, 0, 0, 63, 0, 0, -60, 0, 0, -16, 0, 0, 98, 0, 0, -92, 0, 0, -24, 0, 0, 150, 0, 0, -140, 0, 0, -36, 0, 0, 224, 0, 0, -208
(list; graph; listen)
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OFFSET
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0,11
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FORMULA
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Expansion of 1 + eta(q^3) * eta(q^18)^3 / (eta(q^6) * eta(q^9)^3) in powers of q.
Expansion of 1 + q * chi(-q^3) / chi(-q^9)^3 = psi(q) * chi(-q^3) / phi(-q^9) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
Expansion of eta(q^2)^2 * eta(q^3) * eta(q^18) / (eta(q) * eta(q^6) * eta(q^9)^2) in powers of q.
Euler transform of period 18 sequence [ 1, -1, 0, -1, 1, -1, 1, -1, 2, -1, 1, -1, 1, -1, 0, -1, 1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1/(18 t)) = 1.5 / f(t) where q = exp(2 pi i t).
G.f.: Product_{k>0} (1 + x^k)^2 * P(18, x^k) / (P(3, x^k) * P(9, x^k)) where P(n, x) is nth cyclotomic polynomial.
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EXAMPLE
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1 + q - q^4 + 2*q^10 - 2*q^13 - q^16 + 4*q^19 - 4*q^22 - q^25 + 8*q^28 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^18 + A) / (eta(x + A) * eta(x^6 + A) * eta(x^9 + A)^2), n))}
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CROSSREFS
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A092848(n) = a(3*n + 1).
Sequence in context: A002284 A016424 A108913 this_sequence A095808 A079807 A116373
Adjacent sequences: A139029 A139030 A139031 this_sequence A139033 A139034 A139035
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 07 2008
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