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 A384582 #12 Jun 04 2025 09:54:00
%S A384582 1,1,0,1,1,0,1,2,1,0,1,3,3,5,0,1,4,6,12,23,0,1,5,10,22,57,155,0,1,6,
%T A384582 15,36,105,366,1236,0,1,7,21,55,171,651,2853,11286,0,1,8,28,80,260,
%U A384582 1032,4951,25584,116333,0,1,9,36,112,378,1536,7656,43587,259789,1329433,0
%N A384582 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 A384574.
%F A384582 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(4*n-4*j+k,j)/(4*n-4*j+k) * A(n-j,j).
%e A384582 Square array begins:
%e A384582 1, 1, 1, 1, 1, 1, 1, ...
%e A384582 0, 1, 2, 3, 4, 5, 6, ...
%e A384582 0, 1, 3, 6, 10, 15, 21, ...
%e A384582 0, 5, 12, 22, 36, 55, 80, ...
%e A384582 0, 23, 57, 105, 171, 260, 378, ...
%e A384582 0, 155, 366, 651, 1032, 1536, 2196, ...
%e A384582 0, 1236, 2853, 4951, 7656, 11125, 15552, ...
%o A384582 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(4*n-4*j+k, j)/(4*n-4*j+k)*a(n-j, j)));
%Y A384582 Columns k=0..1 give A000007, A384574.
%Y A384582 Cf. A381566, A384580, A384581, A384583.
%K A384582 nonn,tabl
%O A384582 0,8
%A A384582 _Seiichi Manyama_, Jun 04 2025