OFFSET
0,3
COMMENTS
Euler transform of A002593.
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^A002593(k).
a(n) ~ exp(2^(5/3) * 3^(2/3) * Pi * n^(5/6) / (5 * 7^(1/6)) - Pi * sqrt(7*n) / 60 - 7^(7/6) * Pi * n^(1/6) / (1600 * 6^(2/3)) + Zeta(3) / (4*Pi^2) + 3*Zeta(5) / (2*Pi^4)) / (6^(2/3) * 7^(1/12) * n^(7/12)). - Vaclav Kotesovec, Apr 08 2018
MATHEMATICA
nmax = 23; CoefficientList[Series[Product[1/(1 - x^k)^(k^2 (2 k^2 - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d^3 (2 d^2 - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 08 2018
STATUS
approved