This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A206623 #21 Apr 30 2017 07:40:32
%S A206623 1,2,18,88,398,1768,7508,30644,121310,467234,1756080,6457168,23274788,
%T A206623 82381584,286760344,982874120,3320800590,11070619228,36446345198,
%U A206623 118581503192,381552358872,1214868568728,3829841265428,11959828895612,37013411304892,113570015855642
%N A206623 G.f.: Product_{n>0} ( (1+x^n)/(1-x^n) )^(n^3).
%C A206623 Convolution of A023872 and A248882. - _Vaclav Kotesovec_, Aug 19 2015
%H A206623 Seiichi Manyama, <a href="/A206623/b206623.txt">Table of n, a(n) for n = 0..4595</a> (terms 0..1000 from Vaclav Kotesovec)
%H A206623 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 23.
%F A206623 G.f.: exp( Sum_{n>=1} (sigma_4(2*n) - sigma_4(n))/8 * x^n/n ), where sigma_4(n) is the sum of 4th powers of divisors of n (A001159).
%F A206623 Inverse Euler transform has g.f.: x*(2 + 15*x + 46*x^2 + 60*x^3 + 46*x^4 + 15*x^5 + 2*x^6)/(1-x^2)^4.
%F A206623 a(n) ~ (93*Zeta(5))^(59/600) * exp(5/4 * (93*Zeta(5)/2)^(1/5) * n^(4/5) + Zeta'(-3)) / (2^(59/100) * sqrt(5*Pi) * n^(359/600)), where Zeta(5) = A013663, Zeta'(-3) = A259068. - _Vaclav Kotesovec_, Aug 19 2015
%e A206623 G.f.: A(x) = 1 + 2*x + 18*x^2 + 88*x^3 + 398*x^4 + 1768*x^5 + 7508*x^6 +...
%e A206623 where A(x) = (1+x)/(1-x) * (1+x^2)^8/(1-x^2)^8 * (1+x^3)^27/(1-x^3)^27 *...
%e A206623 Also, A(x) = Euler transform of [2,15,54,120,250,405,686,960,1458,...]:
%e A206623 A(x) = 1/((1-x)^2*(1-x^2)^15*(1-x^3)^54*(1-x^4)^120*(1-x^5)^250*(1-x^6)^405*...).
%t A206623 nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(k^3), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 19 2015 *)
%o A206623 (PARI) {a(n)=polcoeff(prod(m=1,n+1,((1+x^m)/(1-x^m+x*O(x^n)))^(m^3)),n)}
%o A206623 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(2*m, 4)-sigma(m, 4))/8*x^m/m)+x*O(x^n)), n)}
%o A206623 (PARI) {a(n)=local(InvEulerGF=x*(2+15*x+46*x^2+60*x^3+46*x^4+15*x^5+2*x^6)/(1-x^2+x*O(x^n))^4);polcoeff(1/prod(k=1,n,(1-x^k+x*O(x^n))^polcoeff(InvEulerGF,k)),n)}
%o A206623 for(n=0,30,print1(a(n),", "))
%Y A206623 Cf. A156616, A206622, A206624, A001159 (sigma_4).
%K A206623 nonn
%O A206623 0,2
%A A206623 _Paul D. Hanna_, Feb 12 2012