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Search: id:A004402
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| A004402 |
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Expansion of (Sum x^(n^2), n = -inf .. inf )^(-1). |
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+0
2
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| 1, -2, 4, -8, 14, -24, 40, -64, 100, -154, 232, -344, 504, -728, 1040, -1472, 2062, -2864, 3948, -5400, 7336, -9904, 13288, -17728, 23528, -31066, 40824, -53408, 69568, -90248, 116624, -150144, 192612, -246256, 313808
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Taylor series for 1/theta_3. Absolute values are coefficients in Taylor series for 1/theta_4.
Euler transform of period 4 sequence [ -2,3,-2,1,...].
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REFERENCES
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G. Almkvist, Asymptotic formulas and generalized Dedekind sums, Exper. Math., 7 (No. 4, 1998), pp. 343-359.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 103.
J. R. Newman, The World of Mathematics, Simon and Schuster, 1956, Vol. I p. 372.
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LINKS
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G. Almkvist, Asymptotic formulas and generalized Dedekind sums.
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FORMULA
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Ramanujan gave an asymptotic formula (see Almkvist).
G.f.: 1/Product_{m>0} ((1-q^(2m))(1+q^(2m-1))^2) = 1/theta_3(q).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(1/sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n)), n))
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^4+A)^2/eta(x^2+A)^5, n))}
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CROSSREFS
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a(n)=(-1)^n*A015128(n).
Sequence in context: A128770 A069252 A069253 this_sequence A015128 A123655 A084683
Adjacent sequences: A004399 A004400 A004401 this_sequence A004403 A004404 A004405
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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