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A143337
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Expansion of K(k) * (6 * E(k) - (1 + 4*k'^2) * 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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1
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1, 24, -72, 96, -168, 144, -288, 192, -360, 312, -432, 288, -672, 336, -576, 576, -744, 432, -936, 480, -1008, 768, -864, 576, -1440, 744, -1008, 960, -1344, 720, -1728, 768, -1512, 1152, -1296, 1152, -2184, 912, -1440, 1344, -2160, 1008, -2304, 1056, -2016, 1872, -1728, 1152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: 1 - 24 * Sum_{k>0} k * (-x)^k / (1 - (-x)^k) = 1 - 24 * Sum_{k>0} (-x)^k / (1 - (-x)^k)^2.
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EXAMPLE
| 1 + 24*q - 72*q^2 + 96*q^3 - 168*q^4 + 144*q^5 - 288*q^6 + 192*q^7 + ...
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PROG
| (PARI) {a(n) = if( n<1, n==0, -(-1)^n * 24 * sigma(n))}
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CROSSREFS
| (-1)^n * A006352(n) = a(n). 24 * A143348(n) = a(n) unless n=0.
Sequence in context: A124717 A126378 A006352 * A183006 A090860 A064200
Adjacent sequences: A143334 A143335 A143336 * A143338 A143339 A143340
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 09 2008
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