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 A381571 #12 Feb 28 2025 07:36:44
%S A381571 1,1,0,1,2,0,1,4,7,0,1,6,18,38,0,1,8,33,104,267,0,1,10,52,206,735,
%T A381571 2232,0,1,12,75,352,1488,6064,21200,0,1,14,102,550,2626,12246,56510,
%U A381571 222556,0,1,16,133,808,4265,21752,112669,581452,2536661,0,1,18,168,1134,6537,35812,198808,1140150,6501267,31010886,0
%N A381571 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 A381572.
%F A381571 A(n,0) = 0^n; A(n,k) = 2*k * Sum_{j=0..n} binomial(2*n-j+2*k,j)/(2*n-j+2*k) * A(n-j,j).
%e A381571 Square array begins:
%e A381571 1, 1, 1, 1, 1, 1, 1, ...
%e A381571 0, 2, 4, 6, 8, 10, 12, ...
%e A381571 0, 7, 18, 33, 52, 75, 102, ...
%e A381571 0, 38, 104, 206, 352, 550, 808, ...
%e A381571 0, 267, 735, 1488, 2626, 4265, 6537, ...
%e A381571 0, 2232, 6064, 12246, 21752, 35812, 55944, ...
%e A381571 0, 21200, 56510, 112669, 198808, 327010, 512934, ...
%o A381571 (PARI) a(n, k) = if(k==0, 0^n, 2*k*sum(j=0, n, binomial(2*n-j+2*k, j)/(2*n-j+2*k)*a(n-j, j)));
%Y A381571 Columns k=0..1 give A000007, A381572.
%Y A381571 Cf. A379598, A381573.
%K A381571 nonn,tabl
%O A381571 0,5
%A A381571 _Seiichi Manyama_, Feb 28 2025