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A145783
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Expansion of (chi(q) * chi(q^15)) / (chi(q^3) * chi(q^5))^2 in powers of q where chi() is a Ramanujan theta function.
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2
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1, 1, 0, -1, -1, -1, 0, 2, 2, -1, -2, 0, 1, 2, 2, -3, -7, -2, 6, 8, 5, -2, -12, -10, 6, 13, 4, -7, -14, -10, 14, 32, 12, -24, -36, -22, 13, 50, 36, -26, -56, -22, 30, 62, 40, -51, -114, -46, 79, 129, 76, -54, -170, -114, 90, 192, 82, -104, -216, -132, 159, 350, 152, -230, -397, -226, 180, 506, 322, -270, -574
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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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^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30))^2 / (eta(q) * eta(q^4) * eta(q^6)^4 * eta(q^10)^4 * eta(q^15) * eta(q^60)) in powers of q.
Euler transform of period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
| 1 + q - q^3 - q^4 - q^5 + 2*q^7 + 2*q^8 - q^9 - 2*q^10 + q^12 + 2*q^13 + ...
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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^3 + A)^2 * eta(x^5 +A)^2 * eta(x^12 + A)^2 * eta(x^20 + A)^2 * eta(x^30 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^2 * eta(x^10 + A)^2 * eta(x^15 + A) * eta(x^60 + A)), n))}
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CROSSREFS
| Convolution inverse of A145782. A145785(n) = a(n) unless n=0.
Sequence in context: A074942 A043754 A144191 * A094022 A145785 A128580
Adjacent sequences: A145780 A145781 A145782 * A145784 A145785 A145786
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 23 2008
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