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Expansion of theta_4(q^2)theta_2(q)^2/(4q^(1/2)) in powers of q.

+0
2

1, 2, -1, -2, 0, -4, -1, 2, -4, 2, 4, 2, 1, -2, 4, 2, 4, 0, -4, 0, -3, 4, -4, -4, 0, -2, 0, -6, 0, 2, -1, -4, 4, -4, -4, 8, 4, 6, 0, 2, -8, 0, 7, 2, 4, 2, 4, 0, 0, -6, 4, 0, -4, 0, 0, 0, 1, -6, -4, 4, -8, -2, -4, 4, 0, 2, -4, -6, 0, -2, 4, -8, 1, 2, 0, 0, 4, 4, 4, -2, 4, 6, 0, -2, 0, -4, -8, 10, 8, 8, -1, 4, 4, 2, -4, -4, -8, 6, 4, -6, 8, -6, 4, 4 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`G.f.: Product_{k>0} (1+x^k)^2(1-x^(2k))^3/(1+x^(2k)).` `Expansion of f(-q^4)f(q)^2 in powers of q where f(-q)=f(-q,-q^2) is a Ramanujan theta function.` `Expansion of q^(-1/4)eta(q^2)^6/(eta(q)^2eta(q^4)) in powers of q.` `Euler transform of period-4 sequence [2,-4,2,-3,...].` `G.f.: Product_{k>0} (1-x^(2k))^3*(1+x^k)^2/(1+x^(2k)).`
	EXAMPLE	`q +2q^5 -q^9 -2q^13 -4q^21 -q^25 +2q^29 -4*q^33 +...`
	PROGRAM	`(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^6/eta(x+A)^2/eta(x^4+A), n))}`
	CROSSREFS	`2a(n)=A080964(4n+1)=2*A072071(4n+1)-A072070(4n+1).` `Adjacent sequences: A080963 A080964 A080965 this_sequence A080967 A080968 A080969` `Sequence in context: A138498 A050319 A132456 this_sequence A023895 A070963 A139158`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Feb 28 2003`

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.

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