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 A309172 #8 Jul 16 2019 03:55:52
%S A309172 1,1,3,7,15,31,64,128,254,496,961,1844,3516,6662,12564,23593,44153,
%T A309172 82385,153351,284857,528235,978148,1809120,3342722,6171318,11385733,
%U A309172 20994298,38693809,71288111,131297855,241761727,445068646,819205061,1507641487,2774307387,5104712633
%N A309172 Expansion of Product_{k>=1} 1/(1 - (1 + x + x^2) * x^k).
%F A309172 G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (1 + x + x^2)^d/d).
%F A309172 a(n) ~ 1/((1 + 2*r + 3*r^2) * QPochhammer[r] * r^(n+1)), where r = A192918. - _Vaclav Kotesovec_, Jul 16 2019
%t A309172 nmax = 35; CoefficientList[Series[Product[1/(1 - (1 + x + x^2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A309172 nmax = 35; CoefficientList[Series[Exp[Sum[x^k Sum[(1 + x + x^2)^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x]
%Y A309172 Cf. A160571, A227681, A309173.
%K A309172 nonn
%O A309172 0,3
%A A309172 _Ilya Gutkovskiy_, Jul 15 2019