A000199 Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q). (Formerly M2285 N0904)

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

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

Vaclav Kotesovec, Table of n, a(n) for n = 1..5000 (terms 1..1001 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 11 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], {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 A324877 A359947

Adjacent sequences: A000196 A000197 A000198 * A000200 A000201 A000202

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Eric W. Weisstein

Status

approved