OFFSET
0,3
COMMENTS
Euler transform of the octahedral numbers (A005900).
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
Eric Weisstein's World of Mathematics, Octahedral Number
OEIS Wiki, Platonic numbers
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(2*k^2+1)/3).
a(n) ~ exp(Zeta'(-1)/3 - Zeta(3)^2 / (360*Zeta(5)) + 2*Zeta'(-3)/3 + (Zeta(3)/(6*2^(3/5) * Zeta(5)^(2/5))) * n^(2/5) + (5*(Zeta(5)/2)^(1/5)/2) * n^(4/5)) * Zeta(5)^(47/450) / (2^(37/450) * sqrt(5*Pi) * n^(136/225)). - Vaclav Kotesovec, Nov 09 2017
MATHEMATICA
nmax=32; CoefficientList[Series[Product[1/(1 - x^k)^(k (2 k^2 + 1)/3), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 18 2016
STATUS
approved