Search: id:A053250
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%I A053250
%S A053250 1,1,0,1,1,1,1,1,0,2,0,2,1,1,1,2,1,3,1,2,1,2,2,3,1,4,0,4,2,3,2,4,1,5,
%T A053250 2,5,3,5,3,5,2,7,2,7,3,6,4,8,3,9,2,9,5,9,5,10,3,12,4,12,5,11,6,13,6,
%U A053250 16,6,15,7,15,8,17,7,19,6,20,9,19,10,22,8,25,9,25,12,25,12,27,11,31
%V A053250 1,1,0,-1,1,1,-1,-1,0,2,0,-2,1,1,-1,-2,1,3,-1,-2,1,2,-2,-3,1,4,0,-4,2,
               3,-2,-4,1,5,
%W A053250 -2,-5,3,5,-3,-5,2,7,-2,-7,3,6,-4,-8,3,9,-2,-9,5,9,-5,-10,3,12,-4,-12,
               5,11,-6,-13,6,
%X A053250 16,-6,-15,7,15,-8,-17,7,19,-6,-20,9,19,-10,-22,8,25,-9,-25,12,25,-12,
               -27,11,31
%N A053250 Coefficients of the '3rd order' mock theta function phi(q)
%D A053250 Leila A. Dragonette, Some asymptotic formulae for the mock theta functions 
               of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500
%D A053250 Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355
%D A053250 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, 
               Narosa Publishing House, New Delhi, 1988, pp. 17, 31
%D A053250 George N. Watson, The final problem: an account of the mock theta functions, 
               J. London Math. Soc., 11 (1936) 55-80
%D A053250 N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. 
               Soc., 1988; p. 55, Eq. (26.12), p. 58, Eq. (26.56).
%F A053250 Consider partitions of n into distinct odd parts. a(n) = number of them 
               for which the largest part minus twice the number of parts is == 
               3 (mod 4) minus the number for which it is == 1 (mod 4).
%F A053250 a(n) = (-1)^n*(A027358(n)-A027357(n)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 12 2006
%F A053250 G.f.: 1+ Sum_{k>0} x^k^2/((1+x^2)(1+x^4)...(1+x^(2k))).
%p A053250 f:=n->q^(n^2)/mul((1+q^(2*i)),i=1..n); add(f(n),n=0..10);
%t A053250 Series[Sum[q^n^2/Product[1+q^(2k), {k, 1, n}], {n, 0, 10}], {q, 0, 100}]
%o A053250 (PARI) {a(n)= local(t); if(n<0, 0, t=1+O(x^n); polcoeff( sum(k=1, sqrtint(n), 
               t*= x^(2*k-1)/ (1+x^(2*k)) +O(x^(n-(k-1)^2+1)), 1), n))} /* Michael 
               Somos Jul 16 2007 */
%Y A053250 Other '3rd order' mock theta functions are at A000025, A053251, A053252, 
               A053253, A053254, A053255.
%Y A053250 Sequence in context: A068320 A111330 A117447 this_sequence A160813 A116664 
               A024161
%Y A053250 Adjacent sequences: A053247 A053248 A053249 this_sequence A053251 A053252 
               A053253
%K A053250 sign,easy
%O A053250 0,10
%A A053250 Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999

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