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 A381567 #15 Feb 28 2025 07:30:44
%S A381567 1,1,0,1,2,0,1,4,5,0,1,6,14,22,0,1,8,27,64,126,0,1,10,44,134,365,884,
%T A381567 0,1,12,65,240,777,2492,7149,0,1,14,90,390,1438,5238,19578,64688,0,1,
%U A381567 16,119,592,2440,9696,40244,172356,641836,0,1,18,152,854,3891,16632,73408,345726,1668686,6888740,0
%N A381567 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 A381568.
%F A381567 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(2*n-2*j+2*k,j)/(n-j+k) * A(n-j,j).
%e A381567 Square array begins:
%e A381567 1, 1, 1, 1, 1, 1, 1, ...
%e A381567 0, 2, 4, 6, 8, 10, 12, ...
%e A381567 0, 5, 14, 27, 44, 65, 90, ...
%e A381567 0, 22, 64, 134, 240, 390, 592, ...
%e A381567 0, 126, 365, 777, 1438, 2440, 3891, ...
%e A381567 0, 884, 2492, 5238, 9696, 16632, 27036, ...
%e A381567 0, 7149, 19578, 40244, 73408, 125035, 203258, ...
%o A381567 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-2*j+2*k, j)/(n-j+k)*a(n-j, j)));
%Y A381567 Columns k=0..1 give A000007, A381568.
%Y A381567 Cf. A381566, A381569.
%K A381567 nonn,tabl
%O A381567 0,5
%A A381567 _Seiichi Manyama_, Feb 28 2025