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A000199 Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
(Formerly M2285 N0904)
4
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; refs; listen; history; text; internal format)
OFFSET

1,2

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

T. D. Noe, Table of n, a(n) for n = 1..1001

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.

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], {2, -1, 2}]

PROG

(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))

CROSSREFS

A000025(2n-1)=a(n). Cf. A000039.

Sequence in context: A078708 A096273 A069981 * A243099 A201932 A161771

Adjacent sequences:  A000196 A000197 A000198 * A000200 A000201 A000202

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Eric W. Weisstein

STATUS

approved

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Last modified March 26 00:51 EDT 2017. Contains 284111 sequences.