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Search: id:A064053
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| A064053 |
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Dragonette's sequence gamma(n). |
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+0
5
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| 1, 0, -4, 4, -4, 4, -4, 8, -4, 0, -4, 8, -4, 0, -4, 4, -4, 0, 0, 8, -4, -4, -4, 8, 0, 0, 0, 4, -4, 0, -4, 8, -4, -4, 0, 8, 0, 0, -8, 4, -8, 0, 4, 8, -4, 0, -8, 8, 0, 0, -4, 4, -4, 0, -4, 12, -4, 0, 0, 8, -4, 0, -8, 0, -4, 4, 4, 8, -4, 0, -12, 8, 0, 0, 0, 4, -4, -4, -4, 8, -8, 0, 0, 8, 4, 4, -8, 0, -4, 0, 0, 4, -4, 0, -8, 12, 0, 0, 4, 0, -4, 0, -4
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Gamma(n) is used to compute coefficients in series expansion of mock theta function f(q) via A[n]==Sum[P[r]gamma[n-r],{r,0,n}], with P the partition function A000041.
Convolution of this sequence and A000041 is A000025. - Michael Somos Jun 19 2003
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REFERENCES
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G. E. Andrews, The theory of partitions, Cambridge University Press, Cambridge, 1998, page 82, Example 5. MR1634067 (99c:11126)
L. A. Dragonette, Some asymptotic formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500. see page 496
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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G.f.: 1+4*Sum_{k>0} (-1)^k*q^(k*(3*k+1)/2)/(1+q^k). - Michael Somos Jun 19 2003
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, 4*polcoeff( sum(k=1, (sqrtint(24*n+1)-1)\6, (-1)^k*x^((3*k^2+k)/2)/(1+x^k), x*O(x^n)), n))} /* Michael Somos Mar 13 2006 */
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CROSSREFS
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Cf. A000025, A000039, A000041, A000199.
a(n) = 4*A096661(n) if n>0.
Adjacent sequences: A064050 A064051 A064052 this_sequence A064054 A064055 A064056
Sequence in context: A103276 A059190 A085142 this_sequence A108893 A048760 A035627
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KEYWORD
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sign
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Aug 28, 2001
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EXTENSIONS
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Entry revised by Michael Somos, Mar 13 2006
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