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.
G.f.: A(x) = 1 + 3*x + 25*x^2 + 210*x^3 + 1881*x^4 + 17303*x^5 +... Illustrate a(n) = [x^n] 1/(sqrt(1-2*x-3*x^2))^(2*n+1): Let G(x) = 1/sqrt(1-2*x-3*x^2) be the g.f. of A002426, then the array of coefficients of x^k in G(x)^(2*n+1) begins: G(x)^1 : [1, 1, 3, 7, 19, 51, 141, 393,...]; G(x)^3 : [1, 3, 12, 40, 135, 441, 1428, 4572,...]; G(x)^5 : [1, 5, 25, 105, 420, 1596, 5880, 21120,...]; G(x)^7 : [1, 7, 42, 210, 966, 4158, 17094, 67782,...]; G(x)^9 : [1, 9, 63, 363, 1881, 9009, 40755, 176319,...]; G(x)^11: [1, 11, 88, 572, 3289, 17303, 85228, 398684,...]; G(x)^13: [1, 13, 117, 845, 5330, 30498, 162214, 814606,...]; G(x)^15: [1, 15, 150, 1190, 8160, 50388, 287470, 1540710,...]; ... in which the main diagonal forms this sequence.
{a(n)=polcoeff(1/sqrt(1-2*x-3*x^2+x*O(x^n))^(2*n+1),n)}
for(n=0,25,print1(a(n),", "))
G.f.: A(x) = x + 2*x^2 + 11*x^3 + 70*x^4 + 503*x^5 + 3864*x^6 + ... Related expansions. A(x)^2 = x^2 + 4*x^3 + 26*x^4 + 184*x^5 + 1407*x^6 + 11280*x^7 + ... A(x)^3 = x^3 + 6*x^4 + 45*x^5 + 350*x^6 + 2844*x^7 + 23814*x^8 + ... where x = A(x) - 2*A(x)^2 - 3*A(x)^3. The square-root of A(x)/x is the g.f. of A222050: sqrt(A(x)/x) = 1 + x + 5*x^2 + 30*x^3 + 209*x^4 + 1573*x^5 + 12478*x^6 + ...
Rest[CoefficientList[InverseSeries[Series[x - 2*x^2 - 3*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 21 2017 *)
{a(n)=polcoeff(serreverse(x - 2*x^2 - 3*x^3 + x^2*O(x^n)),n)}
for(n=1,30,print1(a(n),", "))