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Search: id:A131795
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| A131795 |
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G.f.: Product_{k>0} (1-x^(4k-1))/(1-x^(4k-2)). |
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+0
1
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| 1, 0, 1, -1, 1, -1, 2, -2, 2, -3, 4, -4, 5, -6, 7, -8, 9, -11, 13, -14, 17, -20, 22, -25, 29, -33, 37, -42, 48, -54, 61, -68, 77, -87, 96, -108, 122, -135, 150, -168, 187, -207, 230, -255, 283, -313, 345, -382, 422, -464, 511, -564, 620, -680, 748, -821, 900, -986, 1079, -1182, 1293, -1411, 1542
(list; graph; listen)
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OFFSET
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0,7
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 25, Eq. (20.23).
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FORMULA
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Euler transform of period 4 sequence [ 0, 1, -1, 0, ...].
G.f.: 1+ Sum_{k>0} x^(k^2+k)*(1-x)(1-x^3)...(1-x^(2k-1))/((1-x^2)(1-x^4)...(1-x^(2k))).
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PROGRAM
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(PARI) {a(n)= if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^((k%4==3)-(k%4==2)), 1+x*O(x^n)), n))}
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CROSSREFS
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Sequence in context: A132968 A029075 A029052 this_sequence A035382 A094988 A076269
Adjacent sequences: A131792 A131793 A131794 this_sequence A131796 A131797 A131798
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 16 2007
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