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A132965
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Expansion of f(-q^8) * chi(q)^2 in powers of q where f(), chi() are Ramanujan theta functions.
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1
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1, 2, 1, 2, 4, 4, 5, 6, 8, 10, 12, 14, 17, 22, 24, 30, 36, 40, 48, 56, 65, 76, 88, 100, 116, 134, 152, 174, 200, 226, 257, 292, 328, 372, 420, 472, 532, 598, 668, 750, 840, 936, 1045, 1166, 1296, 1442, 1604, 1776, 1972, 2186, 2416, 2672, 2952, 3256, 3592, 3960
(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 q^(-1/4) * eta(q^2)^4 * eta(q^8) / (eta(q)^2 * eta(q^4)^2) in powers of q.
Euler transform of period 8 sequence [ 2, -2, 2, 0, 2, -2, 2, -1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (256 t)) = 8^(1/2) (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A132966.
G.f.: Product_{k>0} (1 + x^k)^2 * (1 - x^(2*k)) * (1 + x^(4*k)) / (1 + x^(2*k)).
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EXAMPLE
| q + 2*q^5 + q^9 + 2*q^13 + 4*q^17 + 4*q^21 + 5*q^25 + 6*q^29 + 8*q^33 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x*O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^8 + A) / eta(x + A)^2 / eta(x^4 + A)^2, n))}
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CROSSREFS
| Sequence in context: A153898 A108802 A023673 * A022597 A073252 A134005
Adjacent sequences: A132962 A132963 A132964 * A132966 A132967 A132968
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 23 2007
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