OFFSET
0,3
COMMENTS
Euler transform of A000537.
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)^(k^2*(k+1)^2/4).
a(n) ~ exp(-Zeta(3) / (16*Pi^2) + 741*Zeta(5) / (1600*Pi^4) - 250047*Zeta(5)^3 / (5*Pi^14) + 10207918728 * Zeta(5)^5 / (5*Pi^24) + Zeta'(-3)/2 + (-7*(7/2)^(1/6) * Pi / (3200 * 3^(2/3)) + 9261 * 3^(1/3) * (7/2)^(1/6) * Zeta(5)^2 / (40*Pi^9) - 22754277 * 3^(1/3) * (7/2)^(1/6) * Zeta(5)^4 / (2*Pi^19)) * n^(1/6) + (-21 * 3^(2/3) * (7/2)^(1/3) * Zeta(5) / (20*Pi^4) + 31752 * 6^(2/3) * 7^(1/3) * Zeta(5)^3/Pi^14) * n^(1/3) + (sqrt(7/2)*Pi/60 - 567*sqrt(14)*Zeta(5)^2 / Pi^9) * sqrt(n) + 9 * 3^(1/3) * (7/2)^(2/3) * Zeta(5) / Pi^4 * n^(2/3) + 2 * (2/7)^(1/6) * 3^(2/3) * Pi/5 * n^(5/6)) / (2^(1321/1440) * 3^(479/720) * 7^(119/1440) * n^(839/1440) * Pi^(1/240)). - Vaclav Kotesovec, Nov 09 2017
MATHEMATICA
nmax = 27; CoefficientList[Series[Product[1/(1 - x^k)^(k^2 (k + 1)^2/4), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 19 2017
STATUS
approved