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 A382448 #12 Mar 27 2025 10:12:29 %S A382448 1,1,1,1,3,1,1,6,6,1,1,8,15,8,1,1,10,29,29,10,1,1,12,47,73,47,12,1,1, %T A382448 14,69,149,149,69,14,1,1,16,95,265,371,265,95,16,1,1,18,125,429,785, %U A382448 785,429,125,18,1,1,20,159,649,1479,1941,1479,649,159,20,1 %N A382448 Triangle read by rows, defined by the two-variable g.f. (x^3*y^2 + x^3*y + 1)/(1 - x^2*y - x*y - x). %C A382448 Every row is symmetric. %e A382448 Triangle begins: %e A382448 [0] [1] %e A382448 [1] [1, 1] %e A382448 [2] [1, 3, 1] %e A382448 [3] [1, 6, 6, 1] %e A382448 [4] [1, 8, 15, 8, 1] %e A382448 [5] [1, 10, 29, 29, 10, 1] %e A382448 [6] [1, 12, 47, 73, 47, 12, 1] %e A382448 [7] [1, 14, 69, 149, 149, 69, 14, 1] %e A382448 [8] [1, 16, 95, 265, 371, 265, 95, 16, 1] %e A382448 [9] [1, 18, 125, 429, 785, 785, 429, 125, 18, 1] %o A382448 (Sage) %o A382448 y = polygen(QQ, 'y') %o A382448 x = y.parent()[['x']].gen() %o A382448 gf = (x^3*y^2 + x^3*y + 1)/(1 - x^2*y - x*y - x) %o A382448 [list(u) for u in list(gf.O(10))] %Y A382448 Similar to A008288, A103450, A382436 and A382444. Row sums are A105082. %K A382448 nonn,tabl %O A382448 0,5 %A A382448 _F. Chapoton_, Mar 26 2025