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 A381573 #10 Feb 28 2025 07:39:45
%S A381573 1,1,0,1,3,0,1,6,15,0,1,9,39,118,0,1,12,72,326,1206,0,1,15,114,651,
%T A381573 3345,14712,0,1,18,165,1120,6822,40200,204385,0,1,21,225,1760,12123,
%U A381573 81675,547146,3143826,0,1,24,294,2598,19815,145968,1096080,8239938,52580328,0
%N A381573 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381574.
%F A381573 A(n,0) = 0^n; A(n,k) = 3*k * Sum_{j=0..n} binomial(3*n-2*j+3*k,j)/(3*n-2*j+3*k) * A(n-j,j).
%e A381573 Square array begins:
%e A381573 1, 1, 1, 1, 1, 1, ...
%e A381573 0, 3, 6, 9, 12, 15, ...
%e A381573 0, 15, 39, 72, 114, 165, ...
%e A381573 0, 118, 326, 651, 1120, 1760, ...
%e A381573 0, 1206, 3345, 6822, 12123, 19815, ...
%e A381573 0, 14712, 40200, 81675, 145968, 241773, ...
%o A381573 (PARI) a(n, k) = if(k==0, 0^n, 3*k*sum(j=0, n, binomial(3*n-2*j+3*k, j)/(3*n-2*j+3*k)*a(n-j, j)));
%Y A381573 Columns k=0..1 give A000007, A381574.
%Y A381573 Cf. A379598, A381571.
%K A381573 nonn,tabl
%O A381573 0,5
%A A381573 _Seiichi Manyama_, Feb 28 2025