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Search: id:A128486
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| A128486 |
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Expansion of ((b(q)*c(q))^3 -8*(b(q^2)*c(q^2))^3)/27 in powers of q where b(),c() are cubic AGM analog functions. |
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| 1, -14, 9, 52, 6, -126, -40, 136, 81, -84, -564, 468, 638, 560, 54, -2480, 882, -1134, -556, 312, -360, 7896, -840, 1224, -3089, -8932, 729, -2080, 4638, -756, 4400, 10528, -5076, -12348, -240, 4212, -2410, 7784, 5742, 816, -6870, 5040, 9644, -29328, 486, 11760, -18672, -22320
(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 b(q)*b(q^2)* c(q)*c(q^2)* (b(q)*b(q^2)- c(q)*c(q^2))/9 in powers of q where b(),c() are cubic AGM analog functions.
Expansion of (eta(q)* eta(q^3))^6 -8*(eta(q^2)* eta(q^6))^6 in powers of q.
Expansion of eta(q)*eta(q^2)* eta(q^3)*eta(q^6)* ((eta(q)* eta(q^2))^4 -9*(eta(q^3)* eta(q^6))^4) in powers of q.
G.f.: q Product_{k>0} (1-q^k)^6 (1-q^3k)^6 - 8 q^2 Product_{k>0} (1-q^2k)^6 (1-q^6k)^6.
G.f. is Fourier series of a weight 6 level 6 cusp form. f(-1/(6t)) = 216 t^6 f(t) where q = exp(2 pi i t).
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EXAMPLE
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q - 14*q^2 +9*q^3 + 52*q^4 +6*q^5 - 126*q^6 - 40*q^7 + 136*q^8 + ...
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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^3+A))^6 -8*x*(eta(x^2+A)* eta(x^6+A))^6, n))}
(PARI) {a(n)= local(A, A1, A2); if(n<1, 0, n--; A=x*O(x^n); A1= eta(x+A)* eta(x^2+A); A2= eta(x^3+A)* eta(x^6+A); polcoeff( A1^5*A2 -9*x*A1*A2^5, n))}
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CROSSREFS
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A007332(2n+1)=a(2n+1), A007332(2n)-8*A007332(n)=a(2n).
Sequence in context: A035418 A070602 A086050 this_sequence A147370 A140739 A004503
Adjacent sequences: A128483 A128484 A128485 this_sequence A128487 A128488 A128489
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Mar 04 2007
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