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A000039 Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
(Formerly M0629 N0230)
6

%I M0629 N0230

%S 1,-2,-3,-5,-6,-10,-11,-17,-21,-27,-33,-46,-53,-68,-82,-104,-123,-154,

%T -179,-221,-262,-314,-369,-446,-515,-614,-715,-845,-977,-1148,-1321,

%U -1544,-1778,-2060,-2361,-2736,-3121,-3592,-4097,-4696,-5340,-6105,-6916,-7882,-8919,-10123,-11429,-12952,-14580

%N Coefficient of q^(2n) 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 T. D. Noe, <a href="/A000039/b000039.txt">Table of n, a(n) for n = 0..1000</a>

%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>

%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], {1, -1, 2}]

%o (PARI) a(n)=if(n<0,0,polcoeff(1+sum(k=1,sqrtint(2*n),x^k^2/prod(i=1,k,1+x^i,1+O(x^(2*n)))^2),2*n))

%Y A000025(2n)=a(n). Cf. A000199.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Eric W. Weisstein_

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Last modified February 19 03:37 EST 2018. Contains 299330 sequences. (Running on oeis4.)