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 A378062 #9 Dec 08 2024 17:22:13
%S A378062 0,0,1,0,1,3,0,1,8,20,0,1,15,75,175,0,1,24,189,784,1764,0,1,35,392,
%T A378062 2352,8820,19404,0,1,48,720,5760,29700,104544,226512,0,1,63,1215,
%U A378062 12375,81675,382239,1288287,2760615,0,1,80,1925,24200,196625,1145144,5010005,16359200,34763300
%N A378062 Array read by ascending antidiagonals: A(n, k) = (n + 1)*binomial(2*k + n - 1, k - 1)^2 / (2*k + n - 1) for k > 0, and A(n, 0) = 0.
%e A378062 Array A(n, k) starts:
%e A378062 [0] 0, 1, 3, 20, 175, 1764, 19404, ... A000891
%e A378062 [1] 0, 1, 8, 75, 784, 8820, 104544, ... A145600
%e A378062 [2] 0, 1, 15, 189, 2352, 29700, 382239, ... A145601
%e A378062 [3] 0, 1, 24, 392, 5760, 81675, 1145144, ... A145602
%e A378062 [4] 0, 1, 35, 720, 12375, 196625, 3006003, ... A145603
%e A378062 [5] 0, 1, 48, 1215, 24200, 429429, 7154784, ...
%e A378062 [6] 0, 1, 63, 1925, 44044, 869505, 15767024, ...
%e A378062 [7] 0, 1, 80, 2904, 75712, 1656200, 32626944, ...
%e A378062 .
%e A378062 Seen as a triangle, T(n, k) = A(n-k, k). Compare the descending antidiagonals of A378061.
%e A378062 [0] 0;
%e A378062 [1] 0, 1;
%e A378062 [2] 0, 1, 3;
%e A378062 [3] 0, 1, 8, 20;
%e A378062 [4] 0, 1, 15, 75, 175;
%e A378062 [5] 0, 1, 24, 189, 784, 1764;
%e A378062 [6] 0, 1, 35, 392, 2352, 8820, 19404;
%e A378062 [7] 0, 1, 48, 720, 5760, 29700, 104544, 226512;
%p A378062 A := (n, k) -> ifelse(k = 0, 0, (n + 1)*binomial(2*k + n - 1, k - 1)^2/(2*k + n - 1)):
%p A378062 for n from 0 to 7 do seq(A(n, k), k = 0..7);
%t A378062 A[n_, k_] := If[k==0, 0, (n + 1)*Binomial[2*k + n - 1, k - 1]^2 / (2*k + n - 1)]; Table[A[n-k,k],{n,0,9},{k,0,n}]//Flatten (* _Stefano Spezia_, Dec 08 2024 *)
%Y A378062 Rows: A000891, A145600, A145601, A145602, A145603.
%Y A378062 Columns: A005563, A005565, A378061.
%K A378062 nonn,tabl
%O A378062 0,6
%A A378062 _Peter Luschny_, Dec 07 2024