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 A209405 #8 Jul 01 2025 15:00:47
%S A209405 1,2,3,6,8,15,21,34,47,74,99,151,201,287,383,540,701,970,1255,1688,
%T A209405 2171,2882,3657,4801,6058,7819,9816,12566,15619,19826,24540,30812,
%U A209405 37950,47319,57901,71769,87435,107525,130482,159660,192721,234633,282240,341656,409549
%N A209405 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n*Product_{k=1..n+1} (1-x^k).
%e A209405 G.f.: 1/(1-x) = 1*(1-x) + 2*x*(1-x)*(1-x^2) + 3*x^2*(1-x)*(1-x^2)*(1-x^3) + 6*x^3*(1-x)*(1-x^2)*(1-x^3)*(1-x^4) + 8*x^4*(1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5) +...
%o A209405 (PARI) {a(n)=local(A=[1]); for(i=1,n+1, A=concat(A,0); A[#A]=1-polcoeff(sum(m=1, #A, A[m]*x^m*prod(k=1,m, 1-x^k +x*O(x^#A) )), #A) ); A[n+1]}
%o A209405 for(n=0,50,print1(a(n),", "))
%Y A209405 Cf. A126796.
%K A209405 nonn
%O A209405 0,2
%A A209405 _Paul D. Hanna_, Mar 08 2012