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 A206138 #10 Sep 10 2024 16:10:06
%S A206138 1,1,1,2,2,4,5,8,10,17,21,32,44,62,86,122,164,230,318,428,591,803,
%T A206138 1088,1467,1995,2665,3596,4800,6430,8552,11416,15093,20062,26487,
%U A206138 34988,46035,60626,79490,104278,136337,178189,232331,302724,393493,511165,662775,858380
%N A206138 G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^k.
%e A206138 G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 2*x^4 + 4*x^5 + 5*x^6 + 8*x^7 ...
%e A206138 where
%e A206138 A(x) = 1 + x/(1-x) + x^3/((1-x)*(1-x^2)^2) + x^6/((1-x)*(1-x^2)^2*(1-x^3)^3) + x^10/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4) +...
%o A206138 (PARI) {a(n)=polcoeff(sum(m=0,n,x^(m*(m+1)/2)/prod(k=1,m,(1-x^k +x*O(x^n))^k)),n)}
%o A206138 for(n=0,60,print1(a(n),", "))
%Y A206138 Cf. A206100.
%K A206138 nonn
%O A206138 0,4
%A A206138 _Paul D. Hanna_, Feb 04 2012