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A053258 Coefficients of the '5th order' mock theta function phi_0(q) 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,18

REFERENCES

George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113-134

George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: The mock theta conjectures, Advances in Mathematics, 73 (1989) 242-255

Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 23, 25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) 274-304

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^(2n-1))

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^(2k-1), {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: A031262 A047072 A178058 * A053632 A124060 A140194

Adjacent sequences:  A053255 A053256 A053257 * A053259 A053260 A053261

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified April 20 16:29 EDT 2014. Contains 240807 sequences.