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 A384580 #12 Jun 04 2025 09:52:51
%S A384580 1,1,0,1,1,0,1,2,1,0,1,3,3,3,0,1,4,6,8,10,0,1,5,10,16,27,46,0,1,6,15,
%T A384580 28,54,118,244,0,1,7,21,45,95,228,609,1481,0,1,8,28,68,155,392,1144,
%U A384580 3602,10020,0,1,9,36,98,240,631,1916,6597,23866,74400,0
%N A384580 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 A143500.
%F A384580 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(2*n-2*j+k,j)/(2*n-2*j+k) * A(n-j,j).
%e A384580 Square array begins:
%e A384580 1, 1, 1, 1, 1, 1, 1, ...
%e A384580 0, 1, 2, 3, 4, 5, 6, ...
%e A384580 0, 1, 3, 6, 10, 15, 21, ...
%e A384580 0, 3, 8, 16, 28, 45, 68, ...
%e A384580 0, 10, 27, 54, 95, 155, 240, ...
%e A384580 0, 46, 118, 228, 392, 631, 972, ...
%e A384580 0, 244, 609, 1144, 1916, 3015, 4560, ...
%o A384580 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-2*j+k, j)/(2*n-2*j+k)*a(n-j, j)));
%Y A384580 Columns k=0..2 give A000007, A143500, A384576.
%Y A384580 Cf. A381566, A384581, A384582, A384583.
%K A384580 nonn,tabl
%O A384580 0,8
%A A384580 _Seiichi Manyama_, Jun 04 2025