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 A382880 #13 Apr 12 2025 12:48:15 %S A382880 1,1,1,6,6,1,1,11,33,33,11,1,1,16,85,189,189,85,16,1,1,21,162,590, %T A382880 1107,1107,590,162,21,1,1,26,264,1361,3919,6588,6588,3919,1361,264,26, %U A382880 1,1,31,391,2627,10400,25484,39663,39663,25484,10400,2627,391,31,1 %N A382880 Symmetric triangle read by rows refining A109113. %C A382880 Every row is symmetric. Alternating row sums vanish. %F A382880 G.f.: (1+y)*(1+y*t)/(1-(1+4*y+y^2)*t-(y+y^2+y^3)*t^2). %e A382880 Triangle begins: %e A382880 1, 1; %e A382880 1, 6, 6, 1; %e A382880 1, 11, 33, 33, 11, 1; %e A382880 1, 16, 85, 189, 189, 85, 16, 1; %e A382880 1, 21, 162, 590, 1107, 1107, 590, 162, 21, 1; %e A382880 ... %o A382880 (Sage) %o A382880 y = polygen(QQ,'y') %o A382880 t = LazyPowerSeriesRing(y.parent(),'t').gen() %o A382880 v = (1+y)*(1+y*t)/(1-(1+4*y+y**2)*t-(y+y**2+y**3)*t**2) %o A382880 [list(cf) for cf in v[:8]] %Y A382880 Cf. A109113 (row sums). %K A382880 nonn,tabf %O A382880 0,4 %A A382880 _F. Chapoton_, Apr 07 2025