Search: id:A053260
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%I A053260
%S A053260 0,1,0,1,1,0,1,1,1,1,1,1,1,2,1,2,2,1,2,2,2,3,3,2,3,3,3,3,4,4,4,5,4,5,
%T A053260 5,5,6,6,6,7,7,7,8,9,8,9,10,9,11,11,11,12,13,13,14,15,15,16,17,17,18,
%U A053260 19,19,21,22,22,24,25,25,27,28,29,30,32,32,34,36,36,39,40,41,44,45,46
%N A053260 Coefficients of the '5th order' mock theta function psi_0(q)
%D A053260 George E. Andrews, The fifth and seventh order mock theta functions, 
               Trans. Amer. Math. Soc., 293 (1986) 113-134
%D A053260 George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: 
               The mock theta conjectures, Advances in Mathematics, 73 (1989) 242-255
%D A053260 Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355
%D A053260 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, 
               Narosa Publishing House, New Delhi, 1988, pp. 19, 21, 22
%D A053260 George N. Watson, The mock theta functions (2), Proc. London Math. Soc., 
               series 2, 42 (1937) 274-304
%F A053260 G.f.: psi_0(q) = sum for n >= 0 of q^((n+1)(n+2)/2) (1+q)(1+q^2)...(1+q^n)
%F A053260 a(n) = number of partitions of n such that each part occurs at most twice, 
               the largest part is unique and if k occurs as a part then all smaller 
               positive integers occur
%t A053260 Series[Sum[q^((n+1)(n+2)/2) Product[1+q^k, {k, 1, n}], {n, 0, 12}], {q, 
               0, 100}]
%Y A053260 Other '5th order' mock theta functions are at A053256, A053257, A053258, 
               A053259, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
%Y A053260 Sequence in context: A102382 A024890 A007895 this_sequence A140223 A014643 
               A118382
%Y A053260 Adjacent sequences: A053257 A053258 A053259 this_sequence A053261 A053262 
               A053263
%K A053260 nonn,easy
%O A053260 0,14
%A A053260 Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999

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