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 A182819 #24 Jan 26 2017 02:45:47
%S A182819 1,4,14,39,101,238,533,1131,2314,4566,8763,16376,29939,53612,94302,
%T A182819 163112,277953,467064,774943,1270528,2060331,3306771,5256579,8280649,
%U A182819 12934125,20040761,30817437,47048638,71339593,107469716,160898163
%N A182819 G.f.: exp( Sum_{n>=1} sigma(3n)*x^n/n ).
%C A182819 sigma(3n) = A000203(3n), the sum of divisors of 3n (A144613).
%C A182819 Compare g.f. to P(x), the g.f. of partition numbers (A000041): P(x) = exp( Sum_{n>=1} sigma(n)*x^n/n ).
%C A182819 In general, if r>0 and g.f. = Product_{k>=1} (1 - x^(r*k))/(1 - x^k)^(r+1) then a(n) ~ (r+1-1/r)^((r+1)/4) * exp(Pi*sqrt(2*(r+1-1/r)*n/3)) / (sqrt(r) * 2^((3*r+5)/4) * 3^((r+1)/4) * n^((r+3)/4)). - _Vaclav Kotesovec_, Nov 28 2016
%H A182819 Seiichi Manyama, <a href="/A182819/b182819.txt">Table of n, a(n) for n = 0..1000</a>
%F A182819 Generating function A(x) = E(x^3)/E(x)^4 where E(x) = Product_{n>=1} (1-x^n). [_Joerg Arndt_, Dec 05 2010]
%F A182819 a(n) ~ 11*exp(sqrt(22*n)*Pi/3) / (72*sqrt(6)*n^(3/2)). - _Vaclav Kotesovec_, Nov 26 2016
%F A182819 From _Peter Bala_, Jan 24 2016: (Start)
%F A182819 A(x^3) = P(x)*P(w*x)*P(w^2*x), where P(x) = 1/Product_{n>=1} (1 - x^n) is the g.f. for the partition function p(n) = A000041(n), and where w = exp(2*Pi*i/3) is a primitive cube root of unity.
%F A182819 a(n) = Sum_{j = 0..3*n} ( Sum_{k = 0..3*n-j} w^(j+2*k)*p(k)*p(j) *p(3*n-j-k) ). (End)
%e A182819 G.f.: A(x) = 1 + 4*x + 14*x^2 + 39*x^3 + 101*x^4 + 238*x^5 +...
%e A182819 log(A(x)) = 4*x + 12*x^2/2 + 13*x^3/3 + 28*x^4/4 + 24*x^5/5 + 39*x^6/6 + 32*x^7/7 + 60*x^8/8 +...+ sigma(3n)*x^n/n +...
%p A182819 w := exp(2*Pi*sqrt(-1)*(1/3)):
%p A182819 with(combinat):
%p A182819 seq(simplify(add(add(w^(j+2*k)*numbpart(j)*numbpart(k)*numbpart(3*n-j-k), k = 0..3*n-j), j = 0..3*n)), n = 0..30);
%p A182819 # _Peter Bala_, Jan 24 2017
%t A182819 nmax = 50; CoefficientList[Series[Product[(1 - x^(3*k))/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 26 2016 *)
%o A182819 (PARI) {a(n)=polcoeff(exp(sum(m=1,n,sigma(3*m)*x^m/m)+x*O(x^n)),n)}
%o A182819 (PARI) default(seriesprecision,66); Vec(eta(x^3)/eta(x)^4)\\ _Joerg Arndt_, Dec 06 2010
%Y A182819 Cf. A144613, A000203, A000041; variants: A182818, A182820, A182821.
%K A182819 nonn,easy
%O A182819 0,2
%A A182819 _Paul D. Hanna_, Dec 05 2010