A301981 - OEIS

A301981

Euler transform of A034448.

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 A335714 A215112

Adjacent sequences: A301978 A301979 A301980 * A301982 A301983 A301984

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 30 2018

STATUS

approved