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Search: id:A008440
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| A008440 |
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Expansion of Jacobi theta constant theta_2^6 /(64q^(3/2)). |
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1
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| 1, 6, 15, 26, 45, 66, 82, 120, 156, 170, 231, 276, 290, 390, 435, 438, 561, 630, 651, 780, 861, 842, 1020, 1170, 1095, 1326, 1431, 1370, 1716, 1740, 1682, 2016, 2145, 2132, 2415, 2550, 2353, 2850, 3120, 2810, 3321, 3486, 3285, 3906, 4005, 3722, 4350
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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B. C. Berndt, Fragments by Ramanujan on Lambert series, in Number Theory and Its Applications, K. Gyory and S. Kanemitsu, eds., Kluwer, Dordrecht, 1999, pp. 35-49, see Entry 6.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
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LINKS
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B. C. Berndt, Fragments by Ramanujan on Lambert series.
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FORMULA
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Expansion of Ramanujan phi^6(q) in powers of q.
Expansion of q^(-3/4)(eta(q^2)^2/eta(q))^6 in powers of q.
Euler transform of period 2 sequence [ 6, -6, ...]. - Michael Somos May 23 2006
G.f.: (Sum_{n>=0} x^((n^2+n)/2))^6.
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EXAMPLE
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q^3 +6*q^7 +15*q^11 +26*q^15 +45*q^19 +66*q^23 +82*q^27 +...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( sum(k=0, (sqrtint(8*n+1)-1)\2, x^((k^2+k)/2), x*O(x^n))^6, n))} /* Michael Somos May 23 2006 */
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)^2/eta(x+A))^6, n))} /* Michael Somos May 23 2006 */
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CROSSREFS
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Sequence in context: A051940 A020207 A151762 this_sequence A022601 A112150 A072257
Adjacent sequences: A008437 A008438 A008439 this_sequence A008441 A008442 A008443
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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