Search: id:A000039
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%I A000039 M0629 N0230
%S A000039 1,2,3,5,6,10,11,17,21,27,33,46,53,68,82,104,123,154,179,221,262,314,
%T A000039 369,446,515,614,715,845,977,1148,1321,1544,1778,2060,2361,2736,3121,
%U A000039 3592,4097,4696,5340,6105,6916,7882,8919,10123,11429,12952,14580
%V A000039 1,-2,-3,-5,-6,-10,-11,-17,-21,-27,-33,-46,-53,-68,-82,-104,-123,-154,
               -179,-221,-262,
%W A000039 -314,-369,-446,-515,-614,-715,-845,-977,-1148,-1321,-1544,-1778,-2060,
               -2361,-2736,
%X A000039 -3121,-3592,-4097,-4696,-5340,-6105,-6916,-7882,-8919,-10123,-11429,-12952,
               -14580
%N A000039 Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta 
               function f(q).
%D A000039 L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series 
               of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500.
%D A000039 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000039 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000039 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MockThetaFunction.html">Link to a section of The World of Mathematics.</
               a>
%t A000039 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 A000039 (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 A000039 A000025(2n)=a(n). Cf. A000199.
%Y A000039 Sequence in context: A130714 A130689 A024560 this_sequence A053436 A057546 
               A138587
%Y A000039 Adjacent sequences: A000036 A000037 A000038 this_sequence A000040 A000041 
               A000042
%K A000039 sign
%O A000039 0,2
%A A000039 N. J. A. Sloane (njas(AT)research.att.com).
%E A000039 More terms from Eric Weisstein (eric(AT)weisstein.com)

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