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A053281
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Coefficients of the '10th order' mock theta function phi(q)
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13
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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; internal format)
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OFFSET
| 0,2
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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.
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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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9.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.
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FORMULA
| G.f.: phi(q) = sum for n >= 0 of q^(n(n+1)/2)/((1-q)(1-q^3)...(1-q^(2n+1)))
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MATHEMATICA
| Series[Sum[q^(n(n+1)/2)/Product[1-q^(2k+1), {k, 0, n}], {n, 0, 13}], {q, 0, 100}]
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CROSSREFS
| Other '10th order' mock theta functions are at A053282, A053283, A053284.
Sequence in context: A077768 A143038 A029040 * A094997 A173673 A018125
Adjacent sequences: A053278 A053279 A053280 * A053282 A053283 A053284
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KEYWORD
| nonn,easy
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AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
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