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 A362885 #8 May 20 2023 16:08:42
%S A362885 1,0,1,0,3,1,0,5,6,1,0,7,20,9,1,0,9,56,45,12,1,0,11,144,189,80,15,1,0,
%T A362885 13,352,729,448,125,18,1,0,15,832,2673,2304,875,180,21,1,0,17,1920,
%U A362885 9477,11264,5625,1512,245,24,1,0,19,4352,32805,53248,34375,11664,2401,320,27,1
%N A362885 Array read by ascending antidiagonals: A(n, k) = (1 + 2*n)*k^n.
%F A362885 A(n, k) = A005408(n)*A004248(n, k).
%F A362885 O.g.f. of column k: (1 + k*x)/(1 - k*x)^2.
%F A362885 E.g.f. of column k: exp(k*x)*(1 + 2*k*x).
%F A362885 A(n, n) = A176043(n+1).
%e A362885 The array begins:
%e A362885 1, 1, 1, 1, 1, 1, ...
%e A362885 0, 3, 6, 9, 12, 15, ...
%e A362885 0, 5, 20, 45, 80, 125, ...
%e A362885 0, 7, 56, 189, 448, 875, ...
%e A362885 0, 9, 144, 729, 2304, 5625, ...
%e A362885 0, 11, 352, 2673, 11264, 34375, ...
%e A362885 ...
%t A362885 A[n_,k_]:=(1+2n)k^n; Join[{1}, Table[A[n-k,k],{n,10},{k,0,n}]]//Flatten (* or *)
%t A362885 A[n_,k_]:=SeriesCoefficient[(1+k*x)/(1-k*x)^2,{x,0,n}]; Table[A[n-k,k],{n,0,10},{k,0,n}]//Flatten (* or *)
%t A362885 A[n_,k_]:=n!SeriesCoefficient[Exp[k*x](1+2k*x),{x,0,n}]; Table[A[n-k,k],{n,0,10},{k,0,n}]//Flatten
%Y A362885 Cf. A000007 (k=0), A000012 (n=0), A004248, A005408 (k=1), A008585 (n=1), A014480 (k=2), A033429 (n=2), A058962 (k=4), A124647 (k=3), A155988 (k=9), A171220 (k=5), A176043, A199299 (k=6), A199300 (k=7), A199301 (k=8), A244727 (n=3), A362886 (antidiagonal sums).
%K A362885 nonn,tabl
%O A362885 0,5
%A A362885 _Stefano Spezia_, May 08 2023