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A064053
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Dragonette's sequence gamma(n).
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4
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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
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OFFSET
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0,3
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COMMENTS
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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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Table of n, a(n) for n=0..102.
Eric Weisstein's World of Mathematics, Mock Theta Function.
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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
a(n) = 4 * A096661(n) if n>0.
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EXAMPLE
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1 - 4*x^2 + 4*x^3 - 4*x^4 + 4*x^5 - 4*x^6 + 8*x^7 - 4*x^8 - 4*x^10 + 8*x^11 - 4*x^12 - ...
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PROG
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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, A096661.
Sequence in context: A103276 A059190 A085142 * A108893 A162281 A048760
Adjacent sequences: A064050 A064051 A064052 * A064054 A064055 A064056
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KEYWORD
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sign
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AUTHOR
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Eric W. Weisstein, Aug 28 2001
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EXTENSIONS
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Entry revised by Michael Somos, Mar 13 2006
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STATUS
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approved
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