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 A123261 #10 Sep 05 2022 19:13:40
%S A123261 2,6,450,405168750,10326560651880195445980468750,
%T A123261 17149769349660883198128523550890723880659651223306378240865271303752564539222570800781250
%N A123261 Multiplicative encoding of Motzkin triangle (A026300).
%C A123261 This is to A026300 "Motzkin triangle, T, read by rows; T(0,0) = T(1,0) = T(1,1) = 1; for n >= 2, T(n,0) = 1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k = 1,2,...,n-1 and T(n,n) = T(n-1,n-2) + T(n-1,n-1)" as A007188 "Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i)" is to A007318 "Pascal's triangle read by rows."
%F A123261 a(n) = Product_{i=1..n} p(i+1)^T(n,i), where T(n,i), are as in Motzkin triangle (A026300), T(0,0) = T(1,0) = T(1,1) = 1; for n >= 2, T(n,0) = 1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k = 1,2,...,n-1 and T(n,n) = T(n-1,n-2) + T(n-1,n-1).
%e A123261 a(1) = p(1)^T(1,1) = 2^1 = 2.
%e A123261 a(2) = p(1)^T(2,1) * p(2)^T(2,2) = 2^1 * 3^1 = 6.
%e A123261 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 A123261 a(4) = 2^1 * 3^3 * 5^5 * 7^4 = 405168750.
%e A123261 a(5) = 2^1 * 3^4 * 5^9 * 7^12 * 11^9 = 10326560651880195445980468750.
%e A123261 a(6) = 2^1 * 3^5 * 5^14 * 7^25 * 11^30 * 13^21.
%e A123261 a(7) = 2^1 * 3^6 * 5^20 * 7^44 * 11^69 * 13^76 * 17^51.
%Y A123261 Cf. A000040, A007188, A007318, A009766, A124061, Motzkin numbers (A001006) are T(n, n), other columns of T include A002026, A005322, A005323.
%K A123261 easy,nonn
%O A123261 1,1
%A A123261 _Jonathan Vos Post_, Nov 06 2006