id:A139632 - OEIS Search Results

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

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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	`Expansion of q^(1/4) * eta(q^2)^2 * eta(q^5) / (eta(q) * eta(q^4) * eta(q^10)) 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 A139631.` `G.f.: Product_{k>0} (1 + x^k) / ((1 + x^(2k)) (1 + x^(5*k))).`
	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^2 + A)^2 * eta(x^5 + A) / eta(x + A) / eta(x^4 + A) / eta(x^10 + A), n))}`
	CROSSREFS	`A139631(n) = a(2*n).` `Sequence in context: A086995 A135230 A117957 this_sequence A145704 A145705 A145702` `Adjacent sequences: A139629 A139630 A139631 this_sequence A139633 A139634 A139635`
	KEYWORD	`nonn`
	AUTHOR	`Michael Somos, Apr 27 2008`

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

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