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Search: id:A136599
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| A136599 |
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Expansion of (eta(q) * eta(q^15))^3 in powers of q. |
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1
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| 1, -3, 0, 5, 0, 0, -7, 0, 0, 0, 9, 0, 0, 0, 0, -14, 9, 0, -15, 0, 0, 34, 0, 0, 0, -27, 0, 0, -15, 0, 33, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 45, 0, -14, -15, 0, 25, 0, 0, -86, 0, 0, 0, 66, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 42, 0, 0, 0, -63, 0, 0, -75, 0, 0, 0, 0, 25, 0, 0, 154, 0, 0, 0, 0, 0, 0, 0, 0, -102, -6, 0, -110
(list; graph; listen)
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OFFSET
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2,2
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FORMULA
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Euler transform of period 15 sequence [ -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -6, ...].
G.f. is Fourier series of level 15 weight 3 modular form. f(-1 / (15 t)) = 15^(3/2) (t/i)^3 f(t) where q = exp(2 pi i t).
n=0 or a(n) nonzero iff n in A028955.
G.f.: x^2 * (Product_{k>0} (1 - x^k) * (1 - x^(15*k)))^3.
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EXAMPLE
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q^2 - 3*q^3 + 5*q^5 - 7*q^8 + 9*q^12 - 14*q^17 + 9*q^18 - 15*q^20 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<2, 0, n -= 2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^15 + A))^3, n))}
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CROSSREFS
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Sequence in context: A154725 A010816 A133089 this_sequence A131986 A002656 A166586
Adjacent sequences: A136596 A136597 A136598 this_sequence A136600 A136601 A136602
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jan 11 2008
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