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 A124061 #10 Jul 12 2024 22:19:58 %S A124061 2,6,450,2836181250,81492043057751910481759423160156250, %T A124061 4561157026363824997482074305569280581505536351717093893927260661169357729871499327113563125890139588096951624677718591308593750 %N A124061 Multiplicative encoding of Catalan's triangle: Product p(i+1)^T(n,i). %C A124061 This is to A009766 "Catalan's triangle T(n,k) (read by rows)" as A007188 "Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i)" is to A007318 "Pascal's triangle read by rows." %F A124061 a(n) = Prod[i=i..n] p(i+1)^T(n,i), where T(n,i) are Catalan's triangle as in A009766. %e A124061 a(1) = p(1)^T(1,1) = 2^1 = 2. %e A124061 a(2) = p(1)^T(2,1) * p(2)^T(2,2) = 2^1 * 3^1 = 6. %e A124061 a(3) = p(1)^T(3,1) * p(2)^T(3,2) * p(3)^T(3,3) = 2^1 * 3^2 * 5^2 = 450. %e A124061 a(4) = 2^1 * 3^3 * 5^5 * 7^5 = 2836181250. %e A124061 a(5) = 2^1 * 3^4 * 5^9 * 7^14 * 11^14 = 81492043057751910481759423160156250. %e A124061 a(6) = 2^1 * 3^5 * 5^14 * 7^28 * 11^42 * 13^42. %Y A124061 Cf. A007188, A007318, A009766. %K A124061 easy,nonn %O A124061 1,1 %A A124061 _Jonathan Vos Post_, Nov 03 2006