id:A143240 - OEIS Search Results

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Expansion of Product_{k>0} (1 - x^(3*k)) / (1 - x^(3*k - 1)).

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1, 0, 1, -1, 1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, 1, -1, 0, 0, -1, 1, 1, -1, 1, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, -1, 1, -1, 0, 2, -1, 0, 1, -1 (list; graph; listen)

	OFFSET	`0,101`
	COMMENT	`\|a(n)\|<2 if n<100, \|a(n)\|<3 if n<175.`
	FORMULA	`Euler transform of period 3 sequence [ 0, 1, -1, ...].` `G.f.: Product_{k>0} (1 - x^(3k)) / (1 - x^(3k - 1)).`
	EXAMPLE	`1 + q^2 - q^3 + q^4 + q^10 - q^11 + q^12 - q^13 + q^15 - q^19 + q^20 + ...`
	PROGRAM	`(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, (n+1)\3, (1 - x^(3k)) / (1 - x^(3k - 1)), 1 + x * O(x^n)), n))}`
	CROSSREFS	`Sequence in context: A072943 A072175 A092147 this_sequence A153659 A016102 A083905` `Adjacent sequences: A143237 A143238 A143239 this_sequence A143241 A143242 A143243`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Aug 01 2008`

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Last modified March 15 12:29 EDT 2010. Contains 173428 sequences.

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