

A053266


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


11



0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 9, 10, 12, 12, 14, 15, 17, 18, 20, 21, 25, 26, 29, 31, 35, 36, 41, 43, 48, 51, 56, 59, 66, 70, 76, 81, 89, 94, 103, 109, 119, 126, 137, 144, 158, 167, 180, 191, 207, 218, 236, 250, 269, 285, 306, 323, 349, 368
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OFFSET

0,6


REFERENCES

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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 18, 20, 23


LINKS

Table of n, a(n) for n=0..66.


FORMULA

G.f.: Phi(q) = 1 + sum for n >= 0 of q^(5n^2)/((1q)(1q^4)(1q^6)(1q^9)...(1q^(5n+1)))


MATHEMATICA

Series[Sum[q^(5n^2)/Product[1q^Abs[5k+1], {k, n, n}], {n, 0, 4}], {q, 0, 100}]1


CROSSREFS

Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053267.
Sequence in context: A091372 A185322 A068980 * A112217 A172033 A214131
Adjacent sequences: A053263 A053264 A053265 * A053267 A053268 A053269


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



