Search: id:A053253
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%I A053253
%S A053253 1,2,3,4,6,8,10,14,18,22,29,36,44,56,68,82,101,122,146,176,210,248,
%T A053253 296,350,410,484,566,660,772,896,1038,1204,1391,1602,1846,2120,2428,
%U A053253 2784,3182,3628,4138,4708,5347,6072,6880,7784,8804,9940,11208,12630
%N A053253 Coefficients of the '3rd order' mock theta function omega(q)
%D A053253 Leila A. Dragonette, Some asymptotic formulae for the mock theta functions 
               of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500
%D A053253 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, 
               Narosa Publishing House, New Delhi, 1988, pp. 15, 17, 31
%D A053253 George N. Watson, The final problem: an account of the mock theta functions, 
               J. London Math. Soc., 11 (1936) 55-80
%F A053253 G.f.: omega(q) = sum for n >= 0 of q^(2n(n+1))/((1-q)(1-q^3)...(1-q^(2n+1)))^2
%F A053253 G.f.: Sum_{k>=0} x^k/((1-x)(1-x^3)...(1-x^(2k+1))). - Michael Somos Aug 
               18 2006
%t A053253 Series[Sum[q^(2n(n+1))/Product[1-q^(2k+1), {k, 0, n}]^2, {n, 0, 6}], 
               {q, 0, 100}]
%o A053253 (PARI) {a(n)=local(A); if(n<0, 0, A=1+x*O(x^n); polcoeff( sum(k=0, (sqrtint(2*n+1)-1)\2, 
               A*=(x^(4*k)/(1-x^(2*k+1))^2 +x*O(x^(n-2*(k^2-k))))), n))} /* Michael 
               Somos Aug 18 2006 */
%o A053253 (PARI) {a(n)=local(A); if(n<0, 0, n++; A=1+x*O(x^n); polcoeff( sum(k=0, 
               n-1, A*=(x/(1-x^(2*k+1)) +x*O(x^(n-k)))), n))} /* Michael Somos Aug 
               18 2006 */
%Y A053253 Other '3rd order' mock theta functions are at A000025, A053250, A053251, 
               A053252, A053254, A053255.
%Y A053253 Cf. A095913(n)=a(n-3).
%Y A053253 Sequence in context: A003107 A014977 A008583 this_sequence A095913 A102848 
               A134157
%Y A053253 Adjacent sequences: A053250 A053251 A053252 this_sequence A053254 A053255 
               A053256
%K A053253 nonn,easy
%O A053253 0,2
%A A053253 Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999

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