%I M2285 N0904 #30 Jun 11 2019 12:41:37
%S 1,3,3,7,6,12,13,20,21,34,36,51,58,78,89,118,131,171,197,245,279,349,
%T 398,486,557,671,767,920,1046,1244,1421,1667,1898,2225,2525,2937,3333,
%U 3856,4367,5034,5683,6521,7365,8409,9473,10795,12133,13775,15466
%N Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vaclav Kotesovec, <a href="/A000199/b000199.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..1001 from T. D. Noe)
%H L. A. Dragonette, <a href="http://dx.doi.org/10.1090/S0002-9947-1952-0049927-8">Some Asymptotic Formulae for the Mock Theta Series of Ramanujan</a>, Trans. Amer. Math. Soc., 72 (1952), 474-500.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MockThetaFunction.html">Mock Theta Function.</a>
%F a(n) ~ exp(Pi*sqrt(n/3)) / (2*sqrt(2*n)). - _Vaclav Kotesovec_, Jun 11 2019
%t 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}]
%o (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))
%Y A000025(2n-1)=a(n). Cf. A000039.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Eric W. Weisstein_