id:A143161 - OEIS Search Results

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Expansion of q^(1/6) * eta(q)^2 / (eta(q^2) * eta(q^4)) in powers of q.

+0
1

1, -2, 0, 0, 3, -2, 0, 0, 4, -6, 0, 0, 7, -8, 0, 0, 13, -14, 0, 0, 19, -20, 0, 0, 29, -34, 0, 0, 43, -46, 0, 0, 62, -70, 0, 0, 90, -96, 0, 0, 126, -138, 0, 0, 174, -186, 0, 0, 239, -262, 0, 0, 325, -346, 0, 0, 435, -472, 0, 0, 580, -620, 0, 0, 769, -826, 0, 0, 1007, -1072, 0, 0, 1313, -1408, 0, 0, 1702 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`Expansion of chi(-q)^2 * chi(-q^2) in powers of q where chi() is a Ramanujan theta function.` `Euler transform of period 4 sequence [ -2, -1, -2, 0, ...].` `a(4n + 2) = a(4n + 3) = 0.` `G.f.: (Product_{k>0} (1 + x^k)^2 * (1 + x^(2*k)))^-1.`
	EXAMPLE	`1/q - 2q^5 + 3q^23 - 2q^29 + 4q^47 - 6q^53 + 7q^71 - 8*q^77 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 / eta(x^2 + A) / eta(x^4 + A), n))}`
	CROSSREFS	`A029552(n) = a(4n). -2 A098613(n) = a(4*n + 1).` `Sequence in context: A167634 A113411 A125095 this_sequence A142886 A099026 A053202` `Adjacent sequences: A143158 A143159 A143160 this_sequence A143162 A143163 A143164`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Jul 27 2008`

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Last modified December 20 00:58 EST 2009. Contains 171054 sequences.

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