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A000039 Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
(Formerly M0629 N0230)
5
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

L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500.

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

T. D. Noe, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Mock Theta Function

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 * A053436 A057546 A138587

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 26 06:03 EDT 2017. Contains 288754 sequences.