id:A122858 - OEIS Search Results

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Expansion of E(k)K(k)(2/pi)^2 in powers of q^2 where E(k),K(k) are complete elliptic integrals and q=exp(-pi*K(k')/K(k)).

+0
2

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, -320, 576, -832 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`Expansion of (4P(q^2)-P(q))/3 in powers of q where P() is a Ramanujan Lambert series.` `G.f.: 1 +8Sum_{k>0} x^k/(1+x^k)^2 = 1 -8Sum_{k>0} k(-x)^k/(1-x^k) = 1 +8Sum_{k>0} kx^k(1-3x^k)/(1-x^(2k)).`
	PROGRAM	`(PARI) {a(n)=if(n<1, n==0, -8sumdiv(n, d, (-1)^dd))}`
	CROSSREFS	`A002129(n)*8=a(n) if n>0.` `Adjacent sequences: A122855 A122856 A122857 this_sequence A122859 A122860 A122861` `Sequence in context: A098360 A133038 A143336 this_sequence A053596 A141384 A111218`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Sep 15 2006`

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.

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