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Search: id:A004403
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| A004403 |
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Expansion of 1/theta_3(q)^2 in powers of q. |
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+0
3
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| 1, -4, 12, -32, 76, -168, 352, -704, 1356, -2532, 4600, -8160, 14176, -24168, 40512, -66880, 108876, -174984, 277932, -436640, 679032, -1046016, 1597088, -2418240, 3632992, -5417708, 8022840, -11802176, 17252928, -25070568, 36223424, -52053760, 74414412
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Euler transform of period 4 sequence [ -4,6,-4,2,...].
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FORMULA
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Expansion of (Sum x^(n^2), n = -inf .. inf )^(-2).
Expansion of elliptic function pi / 2K in powers of q.
G.f.: 1/(Sum_{k} x^k^2)^2 = (Product_{k>0} (1+x^(2k))^2/((1-x^k)(1+x^k)^3))^2.
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^2/eta(-x+A)^4, n)) /* Michael Somos Feb 09 2006 */
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CROSSREFS
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Apart from signs, same as A001934. Cf. A015128.
Adjacent sequences: A004400 A004401 A004402 this_sequence A004404 A004405 A004406
Sequence in context: A127811 A138517 A001934 this_sequence A084566 A079769 A107035
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KEYWORD
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sign,easy
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AUTHOR
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njas
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