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 A382444 #28 Mar 26 2025 09:18:10 %S A382444 1,1,1,1,4,1,1,7,7,1,1,9,18,9,1,1,11,34,34,11,1,1,13,54,86,54,13,1,1, %T A382444 15,78,174,174,78,15,1,1,17,106,306,434,306,106,17,1,1,19,138,490,914, %U A382444 914,490,138,19,1,1,21,174,734,1710,2262,1710,734,174,21,1 %N A382444 Triangle read by rows, defined by the two-variable g.f. (1 + y*x^2 + (y^2 + y)*x^3)/(1-(1+y)*x-y*x^2). %C A382444 Every row is symmetric. %e A382444 Triangle begins: %e A382444 [0] [1] %e A382444 [1] [1, 1] %e A382444 [2] [1, 4, 1] %e A382444 [3] [1, 7, 7, 1] %e A382444 [4] [1, 9, 18, 9, 1] %e A382444 [5] [1, 11, 34, 34, 11, 1] %e A382444 [6] [1, 13, 54, 86, 54, 13, 1] %e A382444 [7] [1, 15, 78, 174, 174, 78, 15, 1] %e A382444 [8] [1, 17, 106, 306, 434, 306, 106, 17, 1] %e A382444 [9] [1, 19, 138, 490, 914, 914, 490, 138, 19, 1] %e A382444 ... %o A382444 (Sage) %o A382444 y = polygen(QQ, 'y') %o A382444 x = y.parent()[['x']].gen() %o A382444 gf = (1 + y*x^2 + (y^2 + y)*x^3)/(1 - (1 + y)*x - y*x^2) %o A382444 [list(u) for u in list(gf.O(11))] %Y A382444 Similar to A008288, A103450 and A382436. Row sums are A265107. %K A382444 nonn,tabl %O A382444 0,5 %A A382444 _F. Chapoton_, Mar 25 2025