A000039 - OEIS

A000039

Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
(Formerly M0629 N0230)

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

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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