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 A000039 Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q). (Formerly M0629 N0230) 7
 1, -2, -3, -5, -6, -10, -11, -17, -21, -27, -33, -46, -53, -68, -82, -104, -123, -154, -179, -221, -262, -314, -369, -446, -515, -614, -715, -845, -977, -1148, -1321, -1544, -1778, -2060, -2361, -2736, -3121, -3592, -4097, -4696, -5340, -6105, -6916, -7882, -8919, -10123, -11429, -12952, -14580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..5000 (terms 0..1000 from T. D. Noe) L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500. Eric Weisstein's World of Mathematics, Mock Theta Function FORMULA a(n) ~ -exp(Pi*sqrt(n/3)) / (2*sqrt(2*n)). - Vaclav Kotesovec, Jun 12 2019 MATHEMATICA f[q_, s_] := Sum[q^(n^2)/Product[1+q^k, {k, n}]^2, {n, 0, s}]; Take[CoefficientList[Series[f[q, 100], {q, 0, 100}], q], {1, -1, 2}] PROG (PARI) a(n)=if(n<0, 0, polcoeff(1+sum(k=1, sqrtint(2*n), x^k^2/prod(i=1, k, 1+x^i, 1+O(x^(2*n)))^2), 2*n)) CROSSREFS A000025(2n)=a(n). Cf. A000199. Sequence in context: A130714 A130689 A024560 * A302600 A053436 A057546 Adjacent sequences: A000036 A000037 A000038 * A000040 A000041 A000042 KEYWORD sign AUTHOR N. J. A. Sloane EXTENSIONS More terms from Eric W. Weisstein STATUS approved

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Last modified June 1 17:30 EDT 2023. Contains 363076 sequences. (Running on oeis4.)