id:A139631 - OEIS Search Results

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Expansion of chi(q^5) / chi(-q^2) in powers of q where chi() is a Ramanujan theta function.

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1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 3, 2, 4, 2, 5, 4, 6, 5, 8, 6, 11, 8, 13, 10, 16, 14, 20, 17, 24, 21, 31, 26, 37, 32, 44, 41, 54, 49, 64, 59, 79, 72, 94, 86, 111, 106, 132, 126, 156, 149, 187, 178, 219, 210, 257, 251, 302, 295, 352, 346, 416, 406, 483, 474, 560, 558, 652, 648 (list; graph; listen)

	OFFSET	`0,7`
	FORMULA	`Expansion of q^(1/8) * eta(q^4) * eta(q^10)^2 / (eta(q^2) * eta(q^5) * eta(q^20)) in powers of q.` `G.f. is a period 1 Fourier series which satisfies f(-1 / (640 t)) = 2^(-1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A139632.` `G.f.: Product_{k>0} (1 + x^(2k)) (1 + x^(5k)) / (1 + x^(10k)).`
	EXAMPLE	`1/q + q^15 + q^31 + q^39 + 2q^47 + q^55 + 2q^63 + q^71 + 3*q^79 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^10 + A)^2 / eta(x^2 + A) / eta(x^5 + A) / eta(x^20 + A), n))}`
	CROSSREFS	`A139632(2*n) = a(n).` `Sequence in context: A139024 A025806 A025802 this_sequence A029177 A029176 A029198` `Adjacent sequences: A139628 A139629 A139630 this_sequence A139632 A139633 A139634`
	KEYWORD	`nonn`
	AUTHOR	`Michael Somos, Apr 27 2008`

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Last modified September 6 16:04 EDT 2008. Contains 143483 sequences.

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