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A136028
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Expansion of (phi(q) * phi(q^2))^3 in powers of q where phi() is a Ramanujan theta function.
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1, 6, 18, 44, 90, 144, 212, 288, 330, 418, 528, 588, 836, 1008, 1056, 1440, 1386, 1356, 1894, 1644, 2064, 2880, 2484, 3168, 3428, 2838, 3696, 3864, 4128, 5040, 5280, 5760, 5418, 5656, 5988, 5376, 7678, 8208, 7572, 10080, 8208, 7788, 10560, 8652, 10404
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of (eta(q^2) * eta(q^4))^9 / (eta(q) * eta(q^8))^6 in powers of q.
G.f. is Fourier series of a weight 3 level 8 modular form. f(-1/(8 t)) = 2^(9/2) (t/i)^3 f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1 - x^k)^2 * (1 + x^k)^4 * (1 + x^(2*k)) / (1 + x^(4*k))^2)^3.
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EXAMPLE
| 1 + 6*q + 18*q^2 + 44*q^3 + 90*q^4 + 144*q^5 + 212*q^6 + 288*q^7 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ((eta(x^2 + A) * eta(x^4 + A))^3 / (eta(x + A) * eta(x^8 + A))^2)^3, n))}
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CROSSREFS
| Convolution of A033715 and A097057. a(n) = A029713(n) + 6 * A030207(n).
Sequence in context: A009957 A011929 A070735 * A083719 A182706 A095170
Adjacent sequences: A136025 A136026 A136027 * A136029 A136030 A136031
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Dec 10 2007
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