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A053281 Coefficients of the '10th order' mock theta function phi(q) 14
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

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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

David Newman, A Recurrence inside a Generating Function: Solution to problem 10681, American Mathematical Monthly, vol. 107 (2000), p. 569.

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 A286218 A094997

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 July 27 10:45 EDT 2017. Contains 289847 sequences.