id:A145704 - OEIS Search Results

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Expansion of q^(1/4) * (eta(q^8) * eta(q^10) + eta(q^2) * eta(q^40)) / (eta(q^4) * eta(q^20)) in powers of q.

+0
4

1, 1, 0, -1, 1, 0, 0, -1, 1, 1, -1, -1, 2, 1, -1, -1, 2, 2, -1, -2, 3, 3, -2, -3, 4, 3, -2, -4, 5, 4, -4, -5, 6, 6, -5, -6, 8, 7, -6, -8, 11, 10, -8, -11, 13, 11, -10, -13, 16, 15, -14, -17, 20, 18, -17, -20, 24, 23, -21, -25, 31, 29, -26, -32, 37, 34, -32, -39, 44, 42, -41, -47, 54, 52, -49, -56, 64, 62, -59, -68, 79, 77, -72 (list; graph; listen)

	OFFSET	`0,13`
	FORMULA	`Denoted by "(160~b)" in Simon Norton's replicable function list.` `G.f. is a period 1 Fourier series which satisfies f(-1 / (1280 t)) = f(t) where q = exp(2 pi i t).`
	EXAMPLE	`1/q + q^3 - q^11 + q^15 - q^27 + q^31 + q^35 - q^39 - q^43 + 2*q^47 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^8 + A) * eta(x^10 + A) + x * eta(x^2 + A) * eta(x^40 + A)) / (eta(x^4 + A) * eta(x^20 + A)), n))}`
	CROSSREFS	`A145705(n) = (-1)^n * a(n). A145706(n) = a(2n). A145707(n) = a(2n + 1).` `Sequence in context: A135230 A117957 A139632 this_sequence A145705 A145702 A029339` `Adjacent sequences: A145701 A145702 A145703 this_sequence A145705 A145706 A145707`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Oct 17 2008, Nov 11 2008, Jan 21 2009`

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Last modified December 18 21:37 EST 2009. Contains 171024 sequences.

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