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 A022573 #39 Sep 08 2022 08:44:46
%S A022573 1,8,36,128,394,1088,2776,6656,15155,33056,69508,141568,280382,541696,
%T A022573 1023512,1895424,3446617,6163536,10854400,18846592,32296742,54673920,
%U A022573 91506000,151523840,248403014,403396288,649286724,1036287744,1640796160,2578305024,4022351720,6232177664,9592906446
%N A022573 Expansion of Product_{m>=1} (1+x^m)^8.
%H A022573 Seiichi Manyama, <a href="/A022573/b022573.txt">Table of n, a(n) for n = 0..10000</a>
%F A022573 G.f.: Product_{k>0} (1 + x^k)^8.
%F A022573 Given g.f. A(x), then B(q) = q*A(q^3) satisfies 0 = f(B(q), B(q^2)) where f(u, v) = -u^2 + v + 16*u*v^2. - _Michael Somos_, May 29 2004
%F A022573 Expansion of q^(-1/3) * (eta(q^2) / eta(q))^8 in powers of q.
%F A022573 Euler transform of period 2 sequence [ 8, 0, ...]. - _Michael Somos_, Jun 06 2005
%F A022573 Expansion of chi(-x)^-8 in powers of x where chi() is a Ramanujan theta function.
%F A022573 a(n) ~ exp(2 * Pi * sqrt(2*n/3)) / (16 * 2^(3/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015
%F A022573 a(0) = 1, a(n) = (8/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 03 2017
%F A022573 G.f.: exp(8*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%e A022573 G.f. = 1 + 8*x + 36*x^2 + 128*x^3 + 394*x^4 + 1088*x^5 + 2776*x^6 + ...
%e A022573 G.f. = q + 8*q^4 + 36*q^7 + 128*q^10 + 394*q^13 + 1088*q^16 + 2776*q^19 + ...
%t A022573 a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x]^8, {x, 0, n}]; (* _Michael Somos_, Feb 22 2015 *)
%t A022573 With[{nmax=50}, CoefficientList[Series[Product[(1+q^k)^8, {k,1,nmax}], {q, 0, nmax}],q]] (* _G. C. Greubel_, Feb 26 2018 *)
%o A022573 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) / eta(x + A))^8, n))}; /* _Michael Somos_, May 29 2004 */
%o A022573 (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^8)) \\ _G. C. Greubel_, Feb 26 2018
%o A022573 (Magma) Coefficients(&*[(1+x^m)^8:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 26 2018
%Y A022573 Cf. A000009.
%Y A022573 Column k=8 of A286335.
%K A022573 nonn
%O A022573 0,2
%A A022573 _N. J. A. Sloane_