id:A145727 - OEIS Search Results

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Expansion of f(q) * f(q^15) / (f(-q^6) * f(-q^10)) in powers of q where f() 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^2) * eta(q^30))^3 / (eta(q) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60)) 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^2 + A) * eta(x^30 + A))^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A)), n))}`
	CROSSREFS	`Convolution inverse of A094023. A145726(n) = a(n) unless n=0.` `Sequence in context: A138243 A131796 A131797 this_sequence A145782 A131794 A145726` `Adjacent sequences: A145724 A145725 A145726 this_sequence A145728 A145729 A145730`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Oct 23 2008`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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