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Search: id:A123633
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| A123633 |
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Expansion of (c(q^2)/c(q))^3 in powers of q where c() is a cubic AGM analog function. |
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+0
4
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| 1, -3, 3, 5, -18, 15, 24, -75, 57, 86, -252, 183, 262, -744, 522, 725, -1998, 1365, 1852, -4986, 3336, 4436, -11736, 7719, 10103, -26322, 17067, 22040, -56682, 36306, 46336, -117867, 74700, 94378, -237744, 149277, 186926, -466836, 290706, 361126, -895014, 553224
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Expansion of q/(chi(-q^3)^3/chi(-q))^3 in powers of q where chi() is a Ramanujan theta function.
Euler transform of period 6 sequence [ -3, 0, 6, 0, -3, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v -u*v*(6 + 8*v).
G.f.: x*(Product_{k>0} (1-x^(2k-1))/ (1-x^(6k-3))^3 )^3.
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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+A)/eta(x^2+A))^3*(eta(x^6+A)/eta(x^3+A))^9, n))}
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CROSSREFS
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Convolution inverse of A105559.
Sequence in context: A051684 A139431 A128636 this_sequence A110426 A093310 A132809
Adjacent sequences: A123630 A123631 A123632 this_sequence A123634 A123635 A123636
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 03 2006
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