

A053259


Coefficients of the '5th order' mock theta function phi_1(q)


11



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, 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, 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
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OFFSET

0,26


REFERENCES

George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113134
George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: The mock theta conjectures, Advances in Mathematics, 73 (1989) 242255
Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354355
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 25
George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274304


LINKS

Table of n, a(n) for n=0..100.


FORMULA

G.f.: phi_1(q) = sum for n >= 0 of q^(n+1)^2 (1+q)(1+q^3)...(1+q^(2n1))
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


MATHEMATICA

Series[Sum[q^(n+1)^2 Product[1+q^(2k1), {k, 1, n}], {n, 0, 9}], {q, 0, 100}]


CROSSREFS

Other '5th order' mock theta functions are at A053256, A053257, A053258, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A194297 A100544 A130654 * A194329 A143842 A092876
Adjacent sequences: A053256 A053257 A053258 * A053260 A053261 A053262


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999


STATUS

approved



