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Search: id:A132302
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| A132302 |
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Expansion of q^(-1/2) * eta(q^6)^3/( eta(q) * eta(q^2) * eta(q^3) ) in powers of q. |
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6
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| 1, 1, 3, 5, 10, 15, 26, 39, 63, 92, 140, 201, 295, 415, 591, 818, 1140, 1554, 2126, 2861, 3855, 5126, 6816, 8970, 11793, 15372, 20007, 25857, 33356, 42771, 54734, 69683, 88530, 111968, 141312, 177642, 222842, 278557, 347484, 432095, 536230, 663549
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Euler transform of period 6 sequence [ 1, 2, 2, 2, 1, 0, ...].
Given g.f. A(x), then B(x) = A(x^2) * x satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u^2 - v)^3 - 4 * v^4 * (v - 3*u^2) * (2*v - 3*u^2).
G.f. is a period 1 Fourier series which satisfies f(-1/ (36 t)) = (1/6) g(t) where q = exp(2 pi i t) and g() is g.f. for A132301.
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EXAMPLE
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q + q^3 + 3*q^5 + 5*q^7 + 10*q^9 + 15*q^11 + 26*q^13 + 39*q^15 + ...
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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+A)^3/ eta(x^2+A)/ eta(x^3+A)/ eta(x^6+A), n))}
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CROSSREFS
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Sequence in context: A090491 A126728 A070557 this_sequence A097513 A045513 A008337
Adjacent sequences: A132299 A132300 A132301 this_sequence A132303 A132304 A132305
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 17 2007
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