cp's OEIS Frontend

A279761 Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(2*k^2+1)/3).

%I A279761 #10 Feb 16 2025 08:33:38
%S A279761 1,1,7,26,91,290,946,2922,8937,26521,77485,222005,626988,1743739,
%T A279761 4787625,12979799,34792728,92257673,242197348,629805075,1623197726,
%U A279761 4148192991,10516418844,26458470616,66086152465,163925621199,403931474096,989040788801,2407020523315,5823830868091,14011949899801,33530477120905,79820957945103
%N A279761 Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(2*k^2+1)/3).
%C A279761 Euler transform of the octahedral numbers (A005900).
%H A279761 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A279761 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A279761 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A279761 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctahedralNumber.html">Octahedral Number</a>
%H A279761 OEIS Wiki, <a href="https://oeis.org/wiki/Platonic_numbers">Platonic numbers</a>
%F A279761 G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(2*k^2+1)/3).
%F A279761 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
%t A279761 nmax=32; CoefficientList[Series[Product[1/(1 - x^k)^(k (2 k^2 + 1)/3), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A279761 Cf. A000335, A005900, A023872.
%K A279761 nonn
%O A279761 0,3
%A A279761 _Ilya Gutkovskiy_, Dec 18 2016