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Search: id:A128638
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| A128638 |
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Expansion of (eta(q^6)/eta(q))^5*eta(q^2)/eta(q^3) in powers of q. |
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+0
4
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| 1, 5, 19, 61, 174, 455, 1112, 2573, 5689, 12102, 24900, 49759, 96902, 184408, 343722, 628717, 1130418, 2000669, 3489788, 6005910, 10207688, 17147892, 28494120, 46865519, 76342903, 123236446, 197233723, 313106264, 493231830
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also, expansion of (1/3)*(c(q^2)^2/c(q))/(b(q)^2/b(q^2)) in powers of q, where b(), c() are cubic AGM analog functions.
Also, expansion of q*(psi(q^3)^3/ psi(q))/(phi(-q)^3/ phi(-q^3)) in powers of q, where phi(), psi() are Ramanujan theta functions.
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FORMULA
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Euler transform of period 6 sequence [ 5, 4, 6, 4, 5, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v* (1+8*u)* (1+9*v) -(u-v)^2.
G.f.: x* Product_{k>0} ((1-x^(6k))/ (1-x^k))^5* ((1-x^(2k))/ (1-x^3k)).
G.f. is a period 1 Fourier series which satisfies f(-1 / (6 t)) = (1/72) / f(t) where q = exp(2 pi i t).
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EXAMPLE
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q + 5*q^2 + 19*q^3 + 61*q^4 + 174*q^5 + 455*q^6 + 1112*q^7 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if(n<1, 0, n--; A = x*O(x^n); polcoeff( (eta(x^6+A)/ eta(x+A))^5* eta(x^2+A)/ eta(x^3+A), n))}
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CROSSREFS
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A128639(n) = 8*a(n) unless n = 0. Convolution inverse of A128632.
Sequence in context: A092442 A135266 A124123 this_sequence A036630 A102841 A036637
Adjacent sequences: A128635 A128636 A128637 this_sequence A128639 A128640 A128641
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 16 2007
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EXTENSIONS
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Edited by njas, Apr 01 2008
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