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A006306
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Coefficients of the '2nd-order' mock theta function mu(q).
(Formerly M0163)
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4
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1, -1, 1, 2, -1, -4, 1, 5, -2, -5, 4, 7, -4, -11, 3, 13, -6, -14, 9, 18, -7, -24, 8, 29, -14, -32, 17, 38, -18, -50, 20, 58, -25, -63, 33, 77, -35, -94, 36, 108, -48, -122, 60, 141, -63, -170, 70, 195, -87, -215, 101, 250, -110, -294, 124, 333, -146, -371, 173, 424, -190, -492, 206, 554, -245, -617, 283
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OFFSET
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0,4
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COMMENTS
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Coefficients of the "second-order" mock theta function mu(q).
|a(n)| is the number of partitions of n without repeated odd parts whose M2-rank is even minus the number of partitions of n without repeated odd parts whose M2-rank is odd. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: Sum_{n >= 0} (-1)^n q^n^2 (1-q)(1-q^3)...(1-q^(2n-1))/((1+q^2)^2 (1+q^4)^2 ... (1+q^(2n))^2).
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EXAMPLE
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G.f. = 1 - x + x^2 + 2*x^3 - x^4 - 4*x^5 + x^6 + x*x^7 - 2*x^8 - 5*x^9 + ...
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MATHEMATICA
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CoefficientList[Series[Sum[(-q)^n^2 Product[(1-q^(2k-1))/(1+q^(2k))^2, {k, 1, n}], {n, 0, 10}], {q, 0, 100}], q]
a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ (-1)^k x^k^2 QPochhammer[ x, x^2, k] / QPochhammer[- x^2, x^2, k]^2, {k, 0, Sqrt[n]}], {x, 0, n}]]; (* Michael Somos, Jul 09 2015 *)
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CROSSREFS
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KEYWORD
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sign,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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