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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

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

Dean Hickerson, A proof of the mock theta conjectures, Inventiones Mathematicae, 94 (1988) 639-660

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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22

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..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

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Last modified October 24 13:22 EDT 2014. Contains 248516 sequences.