id:A116916 - OEIS Search Results

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Expansion of q^(-1/8) * (eta(q)^3 + 3 * eta(q^9)^3) in powers of q^3.

+0
4

1, 5, -7, 0, 0, -11, 0, 13, 0, 0, 0, 0, 17, 0, 0, -19, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, -43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`a(5n+3)=a(5n+4)=0. a(25n+1)=5a(n).` `Expansion of f(-q) * a(q) in powers of q where f() is a Ramnaujan theta function and a() is a cubic AGM function.` `Expansion of f(-q)^3 + 3 * q * f(-q^9)^3 in powers of q^3 where f() is a Ramanujan theta function.` `G.f.: Sum_{k} (-1)^k * (6k+1) x^(k * (3*k+1) / 2).`
	EXAMPLE	`q + 5q^25 - 7q^49 - 11q^121 + 13q^169 + 17q^289 - 19q^361 +...`
	PROGRAM	`(PARI) {a(n)=if(issquare(24n+1, &n), n kronecker(3, n)* kronecker(-3, n))}` `(PARI) {a(n)=if(n<1, n==0, n=3; polcoeff( eta(x+xO(x^n))^3 +3xeta(x^9+O(x^n))^3, n))}`
	CROSSREFS	`A010816(3*n) = a(n).` `Sequence in context: A042721 A048658 A001111 this_sequence A133079 A080332 A134756` `Adjacent sequences: A116913 A116914 A116915 this_sequence A116917 A116918 A116919`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Feb 26 2006`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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