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A053261
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Coefficients of the '5th order' mock theta function psi_1(q)
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11
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1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 20, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 34, 35, 37, 39, 40, 41, 44, 45, 47, 50, 51, 53, 56, 58, 60, 63, 65
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OFFSET
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0,7
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REFERENCES
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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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 19, 21, 22
George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274-304
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LINKS
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Table of n, a(n) for n=0..79.
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FORMULA
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G.f.: psi_1(q) = sum for n >= 0 of q^(n(n+1)/2) (1+q)(1+q^2)...(1+q^n)
a(n) = number of partitions of n such that each part occurs at most twice and if k occurs as a part then all smaller positive integers occur
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MATHEMATICA
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Series[Sum[q^(n(n+1)/2) Product[1+q^k, {k, 1, n}], {n, 0, 13}], {q, 0, 100}]
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PROG
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(PARI)
N = 66; x = 'x + O('x^N);
gf = sum(n=0, N, x^(n*(n+1)/2) * prod(k=1, n, 1+x^k) );
v = Vec(gf)
/* Joerg Arndt, Apr 21 2013 */
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CROSSREFS
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Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053262, A053263, A053264, A053265, A053266, A053267.
Sequence in context: A165640 A082892 A025839 * A123584 A112689 A190353
Adjacent sequences: A053258 A053259 A053260 * A053262 A053263 A053264
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KEYWORD
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nonn,easy
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
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STATUS
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approved
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