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 A200539 #13 Feb 23 2023 14:11:58
%S A200539 1,1,4,12,45,168,663,2667,10982,45925,194732,834912,3614063,15771795,
%T A200539 69316740,306534564,1362986799,6089916936,27328613142,123118156260,
%U A200539 556626199974,2524659817449,11484671681511,52384730922720,239534402969925,1097805759803893,5042014405418968
%N A200539 Product of Fibonacci and Motzkin numbers: a(n) = A000045(n+1)*A001006(n).
%C A200539 The g.f. for the Fibonacci numbers is 1/(1-x-x^2) and the g.f. M(x) for the Motzkin numbers satisfies: M(x) = 1 + x*M(x) + x^2*M(x)^2.
%e A200539 G.f.: A(x) = 1 + x + 4*x^2 + 12*x^3 + 45*x^4 + 168*x^5 + 663*x^6 +...
%e A200539 where A(x) = 1*1 + 1*1*x + 2*2*x^2 + 3*4*x^3 + 5*9*x^4 + 8*21*x^5 + 13*51*x^6 + 21*127*x^7 + 34*323*x^8 +...+ A000045(n+1)*A001006(n)*x^n +...
%o A200539 (PARI) {A001006(n)=polcoeff((1-x-sqrt((1-x)^2-4*x^2+x^3*O(x^n)))/(2*x^2),n)}
%o A200539 {a(n)=fibonacci(n+1)*A001006(n)}
%Y A200539 Cf. A098614, A200538, A200540, A098616.
%K A200539 nonn
%O A200539 0,3
%A A200539 _Paul D. Hanna_, Nov 18 2011