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A153155
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Coefficients of the eighth-order mock theta function T_0(q).
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8
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0, 0, 1, -1, 1, -1, 2, -2, 3, -4, 4, -5, 7, -7, 9, -11, 12, -15, 18, -20, 24, -28, 32, -37, 43, -48, 56, -65, 72, -83, 95, -106, 122, -138, 154, -174, 197, -220, 247, -278, 309, -346, 388, -430, 480, -535, 592, -659, 732, -808, 896, -992, 1094, -1209, 1335
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OFFSET
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0,7
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LINKS
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FORMULA
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G.f.: Sum{n >= 0} q^((n+1)(n+2)) (1+q^2)(1+q^4)...(1+q^(2n))/(1+q)(1+q^3)...(1+q^(2n+1)).
a(n) ~ (-1)^n * exp(Pi*sqrt(n)/2) / (2^(11/4) * sqrt(1 + sqrt(2)) * sqrt(n)). - Vaclav Kotesovec, Jun 14 2019
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Sum[x^((k+1)*(k+2)) * Product[(1 + x^(2*j)), {j, 1, k}] / Product[(1 + x^(2*j+1)), {j, 0, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 13 2019 *)
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PROG
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(PARI) lista(nn) = {my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^((n+1)*(n+2)) * prod(k = 1, n, 1 + q^(2*k)) / prod(k = 0, n, 1 + q^(2*k+1))); for (i=0, nn, print1(polcoeff(gf, i), ", "); ); } \\ Michel Marcus, Jun 18 2013
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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