A301982 Expansion of Product_{k>=1} (1 + x^k)^A034448(k).

1, 1, 3, 7, 12, 26, 52, 92, 170, 310, 541, 945, 1636, 2760, 4639, 7743, 12725, 20795, 33730, 54184, 86547, 137351, 216387, 339069, 528394, 818664, 1262245, 1936835, 2957432, 4496330, 6807191, 10262275, 15411203, 23056461, 34366753, 51047199, 75567600

Offset: 0

Author

Vaclav Kotesovec, Mar 30 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001615, A034448, A156303, A301594, A301981.

Programs

Mathematica

nmax = 30; A034448 = Flatten[{1, Table[Times @@ (1 + Power @@@ FactorInteger[k]),{k, 2, nmax+1}]}]; CoefficientList[Series[Exp[Sum[-(-1)^j/j * Sum[A034448[[k]] * x^(j*k), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x]

Formula

Conjecture: a(n) ~ exp(3 * Pi^(2/3) * n^(2/3) / 2^(5/3)) / (2^(4/3) * sqrt(3) * Pi^(1/6) * n^(2/3)).