# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a258348 Showing 1-1 of 1 %I A258348 #11 Aug 22 2018 10:34:05 %S A258348 1,0,2,6,15,32,79,172,397,860,1879,3986,8462,17586,36408,74366,150875, %T A258348 303006,604511,1195872,2350614,4587484,8898857,17154278,32883109, %U A258348 62679852,118858190,224238730,421021209,786793776,1463796383,2711552690,5002097398,9190449808 %N A258348 Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k-1)). %H A258348 Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 %F A258348 a(n) ~ 1 / (2^(3/2) * 15^(5/48) * Pi^(1/12) * n^(29/48)) * exp(-Zeta'(-1) - Zeta(3)/(4*Pi^2) - 75*Zeta(3)^3 / Pi^8 - 15^(5/4) * Zeta(3)^2 / (2*Pi^5) * n^(1/4) - sqrt(15) * Zeta(3) / Pi^2 * sqrt(n) + 4*Pi / (3*15^(1/4)) * n^(3/4)), where Zeta(3) = A002117, Zeta'(-1) = A084448 = 1/12 - log(A074962). %F A258348 G.f.: exp(Sum_{k>=1} (sigma_3(k) - sigma_2(k))*x^k/k). - _Ilya Gutkovskiy_, Aug 22 2018 %t A258348 nmax=40; CoefficientList[Series[Product[1/(1-x^k)^(k*(k-1)),{k,1,nmax}],{x,0,nmax}],x] %t A258348 Clear[a]; a[n_]:= a[n] = 1/n*Sum[(DivisorSigma[3, k]-DivisorSigma[2, k])*a[n-k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 100}] (* _Vaclav Kotesovec_, Apr 11 2016, following a suggestion of _George Beck_ *) %Y A258348 Cf. A000294, A023871, A258344, A258347, A258349, A258350, A258351, A258352. %K A258348 nonn %O A258348 0,3 %A A258348 _Vaclav Kotesovec_, May 27 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE