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A053281 Coefficients of the '10th order' mock theta function phi(q) 13
1, 2, 2, 3, 4, 4, 6, 7, 8, 10, 12, 14, 16, 20, 22, 26, 31, 34, 40, 46, 52, 60, 68, 76, 87, 98, 110, 124, 140, 156, 174, 196, 216, 242, 270, 298, 332, 368, 406, 449, 496, 546, 602, 664, 728, 800, 880, 962, 1056, 1156, 1262, 1381, 1508, 1644, 1794, 1956, 2128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The alternating sum of the same series, namely phi(q) = sum for n >= 0 of (-1)^n q^(n(n+1)/2)/((1-q)(1-q^3)...(1-q^(2n+1))) = 1+x^3-x^7-x^16+x^24+x^39-x^51-..., where the exponents are given by 5n^2 +/- 2n. See the Amer. Math. Monthly reference.

REFERENCES

Youn-Seo Choi, Tenth order mock theta functions in Ramanujan's lost notebook, Inventiones Mathematicae, 136 (1999) p. 497-569.

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9.

American Mathematical Monthly, vol. 107 (2000), p. 569, Answer to Problem number 10681.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

G.f.: phi(q) = sum for n >= 0 of q^(n(n+1)/2)/((1-q)(1-q^3)...(1-q^(2n+1)))

MATHEMATICA

Series[Sum[q^(n(n+1)/2)/Product[1-q^(2k+1), {k, 0, n}], {n, 0, 13}], {q, 0, 100}]

CROSSREFS

Other '10th order' mock theta functions are at A053282, A053283, A053284.

Sequence in context: A077768 A143038 A029040 * A228117 A094997 A173673

Adjacent sequences:  A053278 A053279 A053280 * A053282 A053283 A053284

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

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Last modified October 24 19:48 EDT 2014. Contains 248516 sequences.