|
Search: id:A000039
|
|
|
| A000039 |
|
Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
(Formerly M0629 N0230)
|
|
+0
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; listen)
|
|
|
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
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
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}]
|
|
PROGRAM
|
(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 this_sequence A053436 A057546 A138587
Adjacent sequences: A000036 A000037 A000038 this_sequence A000040 A000041 A000042
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Eric Weisstein (eric(AT)weisstein.com)
|
|
|
Search completed in 0.002 seconds
|
