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A260984
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Coefficients of the mock theta function chibar(q).
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2
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1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 14, 16, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 44, 48, 52, 56, 60, 64, 68, 74, 80, 84, 90, 96, 104, 110, 118, 126, 134, 144, 152, 162, 172, 184, 196, 208, 220, 234, 248
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OFFSET
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0,2
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REFERENCES
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 17, 4th equation.
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LINKS
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FORMULA
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G.f.: 1 + 2*Sum_{n >= 1} q^(n(n+1)/2)*(1+q)^2(1+q^2)^2...(1+q^(n-1))^2*(1+q^n)/((1+q^3)(1+q^6)...(1+q^(3*n)).
G.f.: -1 + 2*(1/(1-x) + x^6/((1-x)*(1-x^5)*(1-x^7)) + x^24/((1-x)*(1-x^5)*(1-x^7)*(1-x^11)*(1-x^13) + ...). [Ramanujan] - Michael Somos, Sep 13 2016
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EXAMPLE
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G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 4*x^6 + 4*x^7 + 4*x^8 + ...
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MAPLE
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N:= 200: # to get a(0) to a(N)
M:= floor((sqrt(1+8*N)-1)/2):
G:= 1 + 2*add(q^(n*(n+1)/2)*mul((1+q^i)^2, i=1..n-1)*(1+q^n)/mul(1+q^(3*i), i=1..n), n=1..M):
S:= series(G, q, N+1):
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MATHEMATICA
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a[ n_] := If[ n < 1, Boole[n == 0], 2 SeriesCoefficient[ Sum[ x^(6 k^2) QPochhammer[ x^3, x^6, k] / QPochhammer[ x, x^2, 3 k + 1], {k, 0, Sqrt[n/6]}], {x, 0, n}]]; (* Michael Somos, Sep 13 2016 *)
nmax = 100; CoefficientList[Series[1 + 2*Sum[x^(k*(k+1)/2) * Product[(1 + x^j), {j, 1, k-1}]^2 * (1 + x^k) / Product[(1 + x^(3*j)), {j, 1, k}], {k, 1, Floor[Sqrt[2*nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 12 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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