%I A053259
%S A053259 0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,1,1,0,1,2,1,0,1,1,1,1,1,2,
%T A053259 1,1,2,2,1,1,2,2,1,1,2,2,2,1,2,3,2,2,3,3,2,2,2,3,3,2,3,4,2,2,4,4,3,3,
%U A053259 4,4,4,3,4,5,4,4,5,5,4,4,5,6,5,4,6,7,5,5,6,7,6,6,7,7,7,6,8,9,7,7,9
%N A053259 Coefficients of the '5th order' mock theta function phi_1(q)
%D A053259 George E. Andrews, The fifth and seventh order mock theta functions, 
               Trans. Amer. Math. Soc., 293 (1986) 113-134
%D A053259 George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: 
               The mock theta conjectures, Advances in Mathematics, 73 (1989) 242-255
%D A053259 Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355
%D A053259 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, 
               Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 25
%D A053259 George N. Watson, The mock theta functions (2), Proc. London Math. Soc., 
               series 2, 42 (1937) 274-304
%F A053259 G.f.: phi_1(q) = sum for n >= 0 of q^(n+1)^2 (1+q)(1+q^3)...(1+q^(2n-1))
%F A053259 a(n) = number of partitions of n into odd parts such that each occurs 
               at most twice, the largest part is unique and if k occurs as a part 
               then all smaller positive odd numbers occur
%t A053259 Series[Sum[q^(n+1)^2 Product[1+q^(2k-1), {k, 1, n}], {n, 0, 9}], {q, 
               0, 100}]
%Y A053259 Other '5th order' mock theta functions are at A053256, A053257, A053258, 
               A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
%Y A053259 Sequence in context: A081396 A100544 A130654 this_sequence A143842 A092876 
               A024940
%Y A053259 Adjacent sequences: A053256 A053257 A053258 this_sequence A053260 A053261 
               A053262
%K A053259 nonn,easy
%O A053259 0,26
%A A053259 Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999