

A053258


Coefficients of the '5th order' mock theta function phi_0(q)


13



1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 3, 4, 4, 5, 4, 4, 5, 5, 5, 5, 6, 6, 5, 5, 6, 6, 6, 6, 7, 7, 7, 6, 7, 8, 7, 8, 8, 9, 9, 8, 9, 10, 9, 9, 10, 11, 10, 10, 11, 11, 11, 11, 12
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OFFSET

0,18


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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 23, 25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..96.


FORMULA

G.f.: phi_0(q) = sum for n >= 0 of q^n^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 and if k occurs as a part then all smaller positive odd numbers occur


MATHEMATICA

Series[Sum[q^n^2 Product[1+q^(2k1), {k, 1, n}], {n, 0, 10}], {q, 0, 100}]


CROSSREFS

Other '5th order' mock theta functions are at A053256, A053257, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A047072 A178058 A260971 * A053632 A242217 A124060
Adjacent sequences: A053255 A053256 A053257 * A053259 A053260 A053261


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson, Dec 19 1999


STATUS

approved



