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A304992
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G.f.: Sum_{k>=0} A000041(k)^3 * x^k / Sum_{k>=0} A000009(k) * x^k.
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0
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1, 0, 7, 18, 98, 210, 969, 1938, 7037, 15258, 44815, 93180, 262391, 518550, 1311015, 2657328, 6189160, 12124098, 27239760, 52063668, 111630480, 211503288, 432900236, 806091180, 1610854427, 2940167268, 5691072911, 10289144976, 19402974147, 34523231688
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OFFSET
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0,3
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COMMENTS
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In general, if m > 1 and g.f. = Sum_{k>=0} A000041(k)^m * x^k / Sum_{k>=0} A000009(k) * x^k, then a(n, m) ~ exp(Pi*sqrt((2*m^2 - 1)*n/3)) * ((2*m^2 - 1)^(m - 1/2) / (2^(3*m - 1) * 3^(m/2) * m^(2*m - 1) * n^m)).
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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a(n) ~ 289 * sqrt(17/3) * exp(Pi*sqrt(17*n/3)) / (186624*n^3).
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Sum[PartitionsP[k]^3*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A000009, A000041, A133042, A260664, A304873, A304878, A304988.
Sequence in context: A030982 A203381 A207158 * A282092 A197938 A207153
Adjacent sequences: A304989 A304990 A304991 * A304993 A304994 A304995
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, May 23 2018
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STATUS
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approved
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