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A301981
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Euler transform of A034448.
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3
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1, 1, 4, 8, 19, 37, 84, 154, 313, 581, 1109, 2001, 3696, 6518, 11637, 20215, 35173, 60007, 102404, 171960, 288286, 477586, 788527, 1289539, 2101394, 3396594, 5469267, 8747285, 13934572, 22068218, 34815513, 54640049, 85434022, 132964684, 206193983, 318414629
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history;
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OFFSET
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0,3
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
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FORMULA
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G.f.: Product_{k>=1} 1/(1-x^k)^A034448(k).
Conjecture: a(n) ~ exp((3*Pi*n)^(2/3)/2 - 1/2) * A^6 / (2 * 3^(5/6) * Pi^(1/3) * n^(5/6)), where A is the Glaisher-Kinkelin constant A074962.
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MATHEMATICA
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nmax = 40; A034448 = Flatten[{1, Table[Times @@ (1 + Power @@@ FactorInteger[k]), {k, 2, nmax+1}]}]; CoefficientList[Series[Exp[Sum[Sum[A034448[[k]] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A001615, A034448, A156303, A301594, A301982.
Sequence in context: A301746 A163318 A129362 * A083579 A335714 A215112
Adjacent sequences: A301978 A301979 A301980 * A301982 A301983 A301984
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Mar 30 2018
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STATUS
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approved
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