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 A277283 #27 Feb 16 2025 08:33:36
%S A277283 1,6,27,98,315,918,2491,6366,15498,36182,81501,177876,377558,781626,
%T A277283 1582173,3137832,6108051,11687598,22012816,40855674,74799828,
%U A277283 135210868,241511115,426570624,745516240,1290006276,2211202692,3756468658,6327617862,10572763842
%N A277283 Expansion of Product_{n>=1} (1 - x^(6*n))/(1 - x^n)^6 in powers of x.
%H A277283 Seiichi Manyama, <a href="/A277283/b277283.txt">Table of n, a(n) for n = 0..1000</a>
%H A277283 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>
%F A277283 G.f.: Product_{n>=1} (1 - x^(6*n))/(1 - x^n)^6.
%F A277283 G.f.: (x^6; x^6)_inf/((x; x)_inf)^6, where (a; q)_inf is the q-Pochhammer symbol. - _Vladimir Reshetnikov_, Nov 20 2016
%F A277283 a(n) ~ 35*sqrt(35) * exp(sqrt(35*n)*Pi/3) / (3456*sqrt(3)*n^2). - _Vaclav Kotesovec_, Nov 21 2016
%e A277283 G.f.: 1 + 6*x + 27*x^2 + 98*x^3 + 315*x^4 + 918*x^5 + 2491*x^6 + ...
%t A277283 (QPochhammer[x^6, x^6]/QPochhammer[x, x]^6 + O[x]^40)[[3]] (* _Vladimir Reshetnikov_, Nov 20 2016 *)
%t A277283 nmax = 50; CoefficientList[Series[Product[(1 - x^(6*k))/(1 - x^k)^6, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 21 2016 *)
%o A277283 (PARI) first(n)=my(x='x); Vec(prod(k=1, n, (1-x^(6*k))/(1-x^k)^6, 1+O(x^(n+1)))) \\ _Charles R Greathouse IV_, Nov 07 2016
%Y A277283 Cf. Expansion of Product_{n>=1} (1 - x^(k*n))/(1 - x^n)^k in powers of x: A015128 (k=2), A273845 (k=3), A274327 (k=4), A277212 (k=5), this sequence (k=6), A160539 (k=7).
%K A277283 nonn
%O A277283 0,2
%A A277283 _Seiichi Manyama_, Nov 07 2016