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A143336
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Expansion of K(k) * (2 * E(k) - K(k)) * (2/pi)^2 in powers of q where E(k), K(k) are complete elliptic integrals and q = exp(-pi * K(k') / K(k)).
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0
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1, -8, -8, -32, -40, -48, -32, -64, -104, -104, -48, -96, -160, -112, -64, -192, -232, -144, -104, -160, -240, -256, -96, -192, -416, -248, -112, -320, -320, -240, -192, -256, -488, -384, -144, -384, -520, -304, -160, -448, -624, -336, -256, -352, -480, -624, -192, -384, -928, -456, -248, -576, -560, -432
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| The generating function equals 0 when 2 * E(k) = K(k) at q = Lambda = 0.1076539192... (A072558) the "One-Ninth" constant.
Expansion of (P(q) - 2 * P(q^2) + 4 * P(q^4))/3 in powers of q where P() is a Ramanujan Lambert series.
G.f.: 1 - 8 * Sum_{k>0} k * x^k / (1 - (-x)^k) = 1 + 8 * Sum_{k>0} (-x)^k / (1 + (-x)^k)^2.
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EXAMPLE
| 1 - 8*q - 8*q^2 - 32*q^3 - 40*q^4 - 48*q^5 - 32*q^6 - 64*q^7 - 104*q^8 + ...
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PROG
| (PARI) {a(n) = if( n<1, n==0, -(-1)^n * 8 * sumdiv(n, d, (-1)^d * d))}
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CROSSREFS
| (-1)^n * A122858(n) = a(n). -8 * A113184(n) = a(n) unless n=0.
Sequence in context: A077110 A098360 A133038 * A122858 A053596 A141384
Adjacent sequences: A143333 A143334 A143335 * A143337 A143338 A143339
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 09 2008
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