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 A124847 #17 Nov 14 2019 09:11:36 %S A124847 1,1,3,1,6,6,1,9,18,10,1,12,36,40,15,1,15,60,100,75,21,1,18,90,200, %T A124847 225,126,28,1,21,126,350,525,441,196,36,1,24,168,560,1050,1176,784, %U A124847 288,45,1,27,216,840,1890,2646,2352,1296,405,55,1,30,270,1200,3150,5292,5880 %N A124847 Triangle read by rows: T(n,k) = k(k+1)*binomial(n-1, k-1)/2 (1 <= k <= n). %C A124847 Sum of row n gives A049611(n). %C A124847 Triangle is P*A, where P is the Pascal triangle written as a lower triangular matrix and C is the diagonal matrix of the triangular numbers 1, 3, 6, 10, .... %e A124847 First few rows of the triangle: %e A124847 1; %e A124847 1, 3; %e A124847 1, 6, 6; %e A124847 1, 9, 18, 10; %e A124847 1, 12, 36, 40, 15; %e A124847 1, 15, 60, 100, 75, 21; %e A124847 ... %e A124847 Sum of row 3 = 38 = (1 + 9 + 18 + 10) = A049611(3). %p A124847 T:=(n,k)->k*(k+1)*binomial(n-1,k-1)/2: for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form %Y A124847 Cf. A049611. %K A124847 nonn,tabl %O A124847 1,3 %A A124847 _Gary W. Adamson_, Nov 10 2006 %E A124847 Edited by _N. J. A. Sloane_, Nov 24 2006