

A053257


Coefficients of the '5th order' mock theta function f_1(q)


11



1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 3, 2, 3, 4, 4, 4, 4, 5, 5, 4, 5, 6, 6, 6, 7, 8, 7, 7, 8, 9, 10, 9, 10, 12, 11, 11, 13, 14, 14, 15, 16, 17, 17, 16, 19, 21, 20, 21, 23, 25, 25, 25, 27, 29, 30, 30, 32, 35, 35, 35, 39, 41, 41, 43, 45, 49, 50, 49, 53, 57, 58, 59, 63, 67, 68
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OFFSET

0,7


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
Dean Hickerson, A proof of the mock theta conjectures, Inventiones Mathematicae, 94 (1988) 639660
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22
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..80.


FORMULA

G.f.: f_1(q) = sum for n >= 0 of q^(n^2+n)/((1+q)(1+q^2)...(1+q^n))
Consider partitions of n into parts differing by at least 2 and with smallest part at least 2. a(n) = number of them with largest part even minus number with largest part odd


MATHEMATICA

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


CROSSREFS

Other '5th order' mock theta functions are at A053256, A053258, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A087011 A000174 A156268 * A151702 A151552 A160418
Adjacent sequences: A053254 A053255 A053256 * A053258 A053259 A053260


KEYWORD

sign,easy


AUTHOR

Dean Hickerson, Dec 19 1999


STATUS

approved



