id:A145782 - OEIS Search Results

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Expansion of (chi(q^3) * chi(q^5))^2 / (chi(q) * chi(q^15)) in powers of q where chi() is a Ramanujan theta function.

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1, -1, 1, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, -1, 2, -1, -2, 3, -1, -1, 2, -3, 0, 3, -1, -2, 2, 0, -2, 6, -3, -4, 7, -3, -2, 5, -6, -2, 8, -3, -5, 6, -2, -4, 12, -7, -10, 15, -6, -5, 13, -12, -4, 18, -7, -11, 14, -6, -10, 24, -14, -20, 32, -12, -12, 29, -24, -9, 36, -15, -22, 30, -13, -22, 50, -27, -36, 63, -26, -24, 56, -45, -22, 69, -30, -42, 62 (list; graph; listen)

	OFFSET	`0,15`
	FORMULA	`Expansion of eta(q) * eta(q^4) * eta(q^6)^4 * eta(q^10)^4 * eta(q^15) * eta(q^60) / (eta(q^2) * eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30))^2 in powers of q.` `Euler transform of period 60 sequence.` `G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 pi i t).`
	EXAMPLE	`1 - q + q^2 + q^5 - q^6 + q^8 - q^10 - q^13 + 2q^14 - q^15 - 2q^16 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^4 * eta(x^10 + A)^4 * eta(x^15 + A) * eta(x^60 + A) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A) * eta(x^30 + A))^2, n))}`
	CROSSREFS	`Convolution inverse of A145783. -A145726(n) = a(n) unless n=0.` `Sequence in context: A131796 A131797 A145727 this_sequence A131794 A145726 A133674` `Adjacent sequences: A145779 A145780 A145781 this_sequence A145783 A145784 A145785`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Oct 23 2008`

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Last modified December 19 12:50 EST 2009. Contains 171053 sequences.

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