

A053267


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


12



0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 4, 4, 5, 5, 7, 6, 8, 8, 9, 9, 12, 11, 14, 14, 16, 16, 20, 19, 23, 24, 27, 27, 32, 32, 37, 38, 43, 44, 51, 51, 58, 61, 67, 69, 78, 80, 89, 93, 102, 106, 118, 121, 134, 140, 153, 159, 175, 181, 198, 207, 224, 234, 256, 265, 288
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OFFSET

0,9


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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 18, 20


LINKS

Table of n, a(n) for n=0..70.


FORMULA

G.f.: Psi(q) = 1 + sum for n >= 0 of q^(5n^2)/((1q^2)(1q^3)(1q^7)(1q^8)...(1q^(5n+2)))


MATHEMATICA

Series[Sum[q^(5n^2)/Product[1q^Abs[5k+2], {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, A053266.
Sequence in context: A238781 A051275 A025799 * A058768 A127682 A127685
Adjacent sequences: A053264 A053265 A053266 * A053268 A053269 A053270


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson, Dec 19 1999


STATUS

approved



