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 A131047 #7 Dec 29 2023 10:54:22 %S A131047 1,0,2,1,0,3,0,4,0,4,1,0,10,0,5,0,6,0,20,0,6,1,0,21,0,35,0,7,0,8,0,56, %T A131047 0,56,0,8,1,0,36,0,126,0,84,0,9 %N A131047 (1/2) * (A007318 - A007318^(-1)). %C A131047 Row sums = (1, 2, 4, 8, ...). A131047 * (1,2,3, ...) = A087447 starting (1, 4, 10, 24, 56, ...). A generalized set of analogous triangles: (1/(Q+1)) * (P^Q - 1/P), Q an integer, generates triangles with row sums = powers of (Q+1). Cf. A131048, A131049, A131050, A131051 for triangles having Q = 2,3,4 and 5, respectively. %C A131047 A007318, Pascal's triangle, = this triangle + A119467, since one triangle = the zeros or masks of the other. - _Gary W. Adamson_, Jun 12 2007 %F A131047 Let A007318 (Pascal's triangle) = P, then A131047 = (1/2) * (P - 1/P); deleting the right border of zeros. %e A131047 First few rows of the triangle: %e A131047 1; %e A131047 0, 2; %e A131047 1, 0, 3; %e A131047 0, 4, 0, 4; %e A131047 1, 0, 10, 0, 5; %e A131047 0, 6, 0, 20, 0, 6; %e A131047 1, 0, 21, 0, 35, 0, 7; %e A131047 ... %Y A131047 Cf. A131048, A131049, A131050, A131051. %Y A131047 Cf. A119467. %K A131047 nonn,tabl %O A131047 1,3 %A A131047 _Gary W. Adamson_, Jun 12 2007