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A145786
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Expansion of q * chi(q^3) * chi(q^5) / (chi(q) * chi(q^15))^2 in powers of q where chi() is a Ramanujan theta function.
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1
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1, -2, 3, -5, 7, -10, 14, -20, 27, -36, 48, -63, 82, -106, 137, -175, 222, -280, 352, -439, 546, -676, 834, -1024, 1253, -1528, 1857, -2250, 2718, -3276, 3936, -4718, 5640, -6728, 8006, -9507, 11266, -13324, 15726, -18526, 21786, -25574, 29970, -35064, 40961, -47774, 55638, -64701
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60))^2 / (eta(q^2)^4 * eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30)^4) 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
| q - 2*q^2 + 3*q^3 - 5*q^4 + 7*q^5 - 10*q^6 + 14*q^7 - 20*q^8 + 27*q^9 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A))^2 / (eta(x^2 + A)^4 * eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A) * eta(x^30 + A)^4), n))}
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CROSSREFS
| - A145728(n) = a(n) unless n=0. -(-1)^n * A123630(n) = a(n). Convolution inverse of A145788.
Sequence in context: A094023 A123630 A145728 * A035967 A097797 A035975
Adjacent sequences: A145783 A145784 A145785 * A145787 A145788 A145789
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 23 2008
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