id:A145785 - OEIS Search Results

Search: id:A145785

Displaying 1-1 of 1 results found.

page 1

Expansion of q * f(-q^2) * f(-q^30) / (f(q^3) * f(q^5)) in powers of q where f() is a Ramanujan theta function.

+0
1

1, 0, -1, -1, -1, 0, 2, 2, -1, -2, 0, 1, 2, 2, -3, -7, -2, 6, 8, 5, -2, -12, -10, 6, 13, 4, -7, -14, -10, 14, 32, 12, -24, -36, -22, 13, 50, 36, -26, -56, -22, 30, 62, 40, -51, -114, -46, 79, 129, 76, -54, -170, -114, 90, 192, 82, -104, -216, -132, 159, 350, 152, -230, -397, -226, 180, 506, 322, -270, -574, -260 (list; graph; listen)

	OFFSET	`1,7`
	FORMULA	`Expansion of eta(q^2) * eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30) / (eta(q^6) * eta(q^10))^3 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	`q - q^3 - q^4 - q^5 + 2q^7 + 2q^8 - q^9 - 2q^10 + q^12 + 2q^13 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A) * eta(x^30 + A) / (eta(x^6 + A) * eta(x^10 + A))^3, n))}`
	CROSSREFS	`Convolution inverse of A058727. -(-1)^n * A094022(n) = a(n).` `Sequence in context: A144191 A145783 A094022 this_sequence A128580 A129402 A134177` `Adjacent sequences: A145782 A145783 A145784 this_sequence A145786 A145787 A145788`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Oct 23 2008`

page 1

Search completed in 0.002 seconds

Last modified December 8 08:31 EST 2009. Contains 170430 sequences.

AT&T Labs Research