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A301981 Euler transform of A034448. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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.

MATHEMATICA

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]

CROSSREFS

Cf. A001615, A034448, A156303, A301594, A301982.

Sequence in context: A301746 A163318 A129362 * A083579 A215112 A265108

Adjacent sequences:  A301978 A301979 A301980 * A301982 A301983 A301984

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 30 2018

STATUS

approved

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Last modified January 24 07:11 EST 2020. Contains 331189 sequences. (Running on oeis4.)