id:A129134 - OEIS Search Results

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Expansion of (1- phi(-q)*phi(-q^2))/2 in powers of q where phi() is a Ramanujan theta function.

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1, 1, -2, -1, 0, 2, 0, -1, 3, 0, -2, -2, 0, 0, 0, -1, 2, 3, -2, 0, 0, 2, 0, -2, 1, 0, -4, 0, 0, 0, 0, -1, 4, 2, 0, -3, 0, 2, 0, 0, 2, 0, -2, -2, 0, 0, 0, -2, 1, 1, -4, 0, 0, 4, 0, 0, 4, 0, -2, 0, 0, 0, 0, -1, 0, 4, -2, -2, 0, 0, 0, -3, 2, 0, -2, -2, 0, 0, 0, 0, 5, 2, -2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 1, -6, -1, 0, 4, 0, 0, 0 (list; graph; listen)

	OFFSET	`1,3`
	FORMULA	`Expansion of (1- eta(q)^2* eta(q^2)/ eta(q^4))/2 in powers of q.` `G.f.: (1- Product_{k>0} (1-x^k)^2/ (1+x^(2k)) )/2.`
	PROGRAM	`(PARI) {a(n)=if(n<1, 0, (-1)^((n-1)\2)* sumdiv(n, d, kronecker(-8, d)))}` `(PARI) {a(n)= local(A); if(n<1, 0, A=xO(x^n); polcoeff( (1- eta(x+A)^2 eta(x^2+A)/ eta(x^4+A))/2, n))}`
	CROSSREFS	`A002325(n)*(-1)^[(n-1)/2]= a(n).` `Sequence in context: A091392 A036577 A002325 this_sequence A133693 A065675 A127476` `Adjacent sequences: A129131 A129132 A129133 this_sequence A129135 A129136 A129137`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Mar 30 2007`

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Last modified November 24 19:38 EST 2009. Contains 167438 sequences.

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