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

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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

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

Programs

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}]

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))

Formula

a(n) ~ exp(Pi*sqrt(n/3)) / (2*sqrt(2*n)). - Vaclav Kotesovec, Jun 11 2019

Extensions

More terms from Eric W. Weisstein