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 A064053 Dragonette's sequence gamma(n). 5
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. REFERENCES G. E. Andrews, The theory of partitions, Cambridge University Press, Cambridge, 1998, page 82, Example 5. MR1634067 (99c:11126) LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500. See page 496. Eric Weisstein's World of Mathematics, Mock Theta Function. FORMULA G.f.: 1 + 4 * Sum_{k>0} (-1)^k * x^(k*(3*k + 1)/2) / (1 + x^k). - Michael Somos, Jun 19 2003 Convolution of this sequence and A000041 is A000025. - Michael Somos, Jun 19 2003 a(n) = 4 * A096661(n) unless n=0. EXAMPLE G.f. = 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 - ... MATHEMATICA a[ n_]:= SeriesCoefficient[1 +4 *Sum[(-1)^k*x^(k*(3*k+1)/2)/(1+x^k), {k, Quotient[Sqrt[1 +24*n] - 1, 6]}], {x, 0, n}]; (* Michael Somos, Apr 08 2015 *) PROG (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 */ CROSSREFS Cf. A000025, A000039, A000041, A000199, A096661. Sequence in context: A103276 A059190 A085142 * A108893 A162281 A262690 Adjacent sequences:  A064050 A064051 A064052 * A064054 A064055 A064056 KEYWORD sign AUTHOR Eric W. Weisstein, Aug 28 2001 EXTENSIONS Entry revised by Michael Somos, Mar 13 2006 STATUS approved

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Last modified May 11 13:21 EDT 2021. Contains 343791 sequences. (Running on oeis4.)