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 A368506 #11 Dec 28 2023 09:23:14
%S A368506 1,1,0,1,2,0,1,4,3,0,1,6,11,4,0,1,8,24,26,5,0,1,10,42,82,57,6,0,1,12,
%T A368506 65,188,261,120,7,0,1,14,93,360,787,804,247,8,0,1,16,126,614,1870,
%U A368506 3204,2440,502,9,0,1,18,164,966,3810,9476,12900,7356,1013,10,0
%N A368506 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^(n-j) * binomial(j+k-1,j).
%F A368506 G.f. of column k: 1/((1-k*x) * (1-x)^k).
%e A368506 Square array begins:
%e A368506 1, 1, 1, 1, 1, 1, 1, ...
%e A368506 0, 2, 4, 6, 8, 10, 12, ...
%e A368506 0, 3, 11, 24, 42, 65, 93, ...
%e A368506 0, 4, 26, 82, 188, 360, 614, ...
%e A368506 0, 5, 57, 261, 787, 1870, 3810, ...
%e A368506 0, 6, 120, 804, 3204, 9476, 23112, ...
%e A368506 0, 7, 247, 2440, 12900, 47590, 139134, ...
%o A368506 (PARI) T(n, k) = sum(j=0, n, k^(n-j)*binomial(j+k-1, j));
%Y A368506 Columns k=0..3 give A000007, A000027(n+1), A125128(n+1), A052150.
%Y A368506 Main diagonal gives A293574.
%Y A368506 Cf. A008949, A368487.
%K A368506 nonn,tabl
%O A368506 0,5
%A A368506 _Seiichi Manyama_, Dec 27 2023