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A139213
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Expansion of phi(q) * phi(-q^18) / (phi(-q^3) * phi(-q^6)) in powers of q where phi() is a Ramanujan theta function.
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4
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1, 2, 0, 2, 6, 0, 6, 16, 0, 14, 36, 0, 30, 76, 0, 60, 150, 0, 114, 280, 0, 208, 504, 0, 366, 878, 0, 626, 1488, 0, 1044, 2464, 0, 1704, 3996, 0, 2730, 6364, 0, 4300, 9972, 0, 6672, 15400, 0, 10212, 23472, 0, 15438, 35346, 0, 23076, 52644, 0, 34134, 77616, 0, 50008
(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)^5 * eta(q^12) * eta(q^18)^2 / (eta(q)^2 * eta(q^3)^2 * eta(q^4)^2 * eta(q^6) * eta(q^36)) in powers of q.
Euler transform of period 36 sequence [ 2, -3, 4, -1, 2, 0, 2, -1, 4, -3, 2, 1, 2, -3, 4, -1, 2, -2, 2, -1, 4, -3, 2, 1, 2, -3, 4, -1, 2, 0, 2, -1, 4, -3, 2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = (1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A139215.
a(3*n + 2) = 0.
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EXAMPLE
| 1 + 2*q + 2*q^3 + 6*q^4 + 6*q^6 + 16*q^7 + 14*q^9 + 36*q^10 + 30*q^12 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^12 + A) * eta(x^18 + A)^2 / (eta(x + A)^2 * eta(x^3 + A)^2 * eta(x^4 + A)^2 * eta(x^6 + A) * eta(x^36 + A)), n))}
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CROSSREFS
| 2 * A139214(n) = a(n) unless n=0.
Sequence in context: A115951 A057607 A186634 * A033727 A033757 A136426
Adjacent sequences: A139210 A139211 A139212 * A139214 A139215 A139216
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Apr 11 2008
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