id:A143337 - OEIS Search Results

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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, 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; listen)

	OFFSET	`0,2`
	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.`
	EXAMPLE	`1 + 24q - 72q^2 + 96q^3 - 168q^4 + 144q^5 - 288q^6 + 192*q^7 + ...`
	PROGRAM	`(PARI) {a(n) = if( n<1, n==0, -(-1)^n * 24 * sigma(n))}`
	CROSSREFS	`(-1)^n * A006352(n) = a(n). 24 * A143348(n) = a(n) unless n=0.` `Sequence in context: A124717 A126378 A006352 this_sequence A090860 A064200 A042128` `Adjacent sequences: A143334 A143335 A143336 this_sequence A143338 A143339 A143340`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Aug 09 2008`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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