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 A365672 #9 Oct 01 2023 07:13:10 %S A365672 1,1,1,1,7,7,1,22,139,139,1,50,889,5473,5473,1,95,3549,58708,357721, %T A365672 357721,1,161,10794,360940,5771821,34988647,34988647,1,252,27426, %U A365672 1595110,50434901,791512162,4784061619,4784061619 %N A365672 Triangle read by rows. T(n, k) = 1 if k = 0, equals T(n, k-1) if k = n, and otherwise is (n - k + 1) * (2 * (n - k) + 1) * T(n, k - 1) + T(n - 1, k). %C A365672 This triangle is described by _Peter Bala_ (see link). %C A365672 This a weighted generalized Catalan triangle (A365673) with the hexagonal numbers as weights. %H A365672 Peter Bala, <a href="/A126156/a126156.pdf">A triangle for calculating A126156</a>. %e A365672 Triangle T(n, k) starts: %e A365672 [0] 1; %e A365672 [1] 1, 1; %e A365672 [2] 1, 7, 7; %e A365672 [3] 1, 22, 139, 139; %e A365672 [4] 1, 50, 889, 5473, 5473; %e A365672 [5] 1, 95, 3549, 58708, 357721, 357721; %e A365672 [6] 1, 161, 10794, 360940, 5771821, 34988647, 34988647; %e A365672 [7] 1, 252, 27426, 1595110, 50434901, 791512162, 4784061619, 4784061619; %p A365672 T := proc(n, k) option remember; if k = 0 then 1 else if k = n then T(n, k-1) else (n - k + 1) * (2 * (n - k) + 1) * T(n, k - 1) + T(n - 1, k) fi fi end: %Y A365672 Cf. A000384, A126156 (main diagonal), A365673 (general case). %K A365672 nonn,tabl %O A365672 0,5 %A A365672 _Peter Luschny_, Sep 29 2023