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A053256
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Coefficients of the '5th order' mock theta function f_0(q)
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11
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1, 1, -1, 1, 0, 0, -1, 1, 0, 1, -2, 1, -1, 2, -2, 2, -1, 1, -3, 2, -1, 3, -3, 2, -2, 3, -4, 3, -3, 4, -5, 5, -3, 5, -7, 5, -5, 6, -7, 7, -6, 7, -9, 9, -7, 9, -11, 9, -9, 11, -13, 12, -11, 13, -15, 15, -13, 16, -19, 17, -17, 19, -21, 21, -20, 22, -26, 25, -23, 27, -30, 29, -28, 32, -35, 34, -34, 36, -41, 40, -38, 44, -48, 46
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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REFERENCES
| George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113-134
George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: The mock theta conjectures, Advances in Mathematics, 73 (1989) 242-255
Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 22, 23
George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274-304
Dean Hickerson, A proof of the mock theta conjectures, Inventiones Mathematicae, 94 (1988) 639-660
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FORMULA
| G.f.: 1 + Sum_{k>0} q^k^2 / ((1 + q) * (1 + q^2) * ... * (1 + q^k)).
Consider partitions of n into parts differing by at least 2. a(n) = number of them with largest part odd minus number with largest part even
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EXAMPLE
| 1 + x - x^2 + x^3 - x^6 + x^7 + x^9 - 2*x^10 + x^11 - x^12 + 2*x^13 - ...
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MATHEMATICA
| Series[Sum[q^n^2/Product[1+q^k, {k, 1, n}], {n, 0, 10}], {q, 0, 100}]
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PROG
| (PARI) {a(n) = local(t); if( n<0, 0, t = 1 + O(x^n); polcoeff( sum( k=1, sqrtint(n), t *= x^(2*k-1) / (1 + x^k + O(x^(n - (k-1)^2 + 1))), 1), n))} /* Michael Somos, Mar 12 2006 */
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CROSSREFS
| Other '5th order' mock theta functions are at A053257, A053258, A053259, A053260, A053261, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A123245 A110535 A033941 * A102418 A106032 A003646
Adjacent sequences: A053253 A053254 A053255 * A053257 A053258 A053259
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KEYWORD
| sign,easy,changed
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AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
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