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

%I A000199 M2285 N0904 #31 Feb 16 2025 08:32:20
%S A000199 1,3,3,7,6,12,13,20,21,34,36,51,58,78,89,118,131,171,197,245,279,349,
%T A000199 398,486,557,671,767,920,1046,1244,1421,1667,1898,2225,2525,2937,3333,
%U A000199 3856,4367,5034,5683,6521,7365,8409,9473,10795,12133,13775,15466
%N A000199 Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
%D A000199 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000199 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000199 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 A000199 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 A000199 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MockThetaFunction.html">Mock Theta Function.</a>
%F A000199 a(n) ~ exp(Pi*sqrt(n/3)) / (2*sqrt(2*n)). - _Vaclav Kotesovec_, Jun 11 2019
%t A000199 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 A000199 (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 A000199 A000025(2n-1)=a(n). Cf. A000039.
%K A000199 nonn
%O A000199 1,2
%A A000199 _N. J. A. Sloane_
%E A000199 More terms from _Eric W. Weisstein_