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Search: id:A000199
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| A000199 |
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Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
(Formerly M2285 N0904)
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+0
4
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| 1, 3, 3, 7, 6, 12, 13, 20, 21, 34, 36, 51, 58, 78, 89, 118, 131, 171, 197, 245, 279, 349, 398, 486, 557, 671, 767, 920, 1046, 1244, 1421, 1667, 1898, 2225, 2525, 2937, 3333, 3856, 4367, 5034, 5683, 6521, 7365, 8409, 9473, 10795, 12133, 13775, 15466
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
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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], {2, -1, 2}]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, polcoeff(1+sum(k=1, sqrtint(2*n-1), x^k^2/prod(i=1, k, 1+x^i, 1+O(x^(2*n-1)))^2), 2*n-1))
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CROSSREFS
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A000025(2n-1)=a(n). Cf. A000039.
Sequence in context: A078708 A096273 A069981 this_sequence A161771 A160515 A105670
Adjacent sequences: A000196 A000197 A000198 this_sequence A000200 A000201 A000202
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Eric Weisstein (eric(AT)weisstein.com)
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