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 A384581 #10 Jun 04 2025 09:53:56
%S A384581 1,1,0,1,1,0,1,2,1,0,1,3,3,4,0,1,4,6,10,16,0,1,5,10,19,41,92,0,1,6,15,
%T A384581 32,78,224,616,0,1,7,21,50,131,411,1464,4729,0,1,8,28,74,205,672,2617,
%U A384581 11002,40776,0,1,9,36,105,306,1031,4170,19251,93234,388057,0
%N A384581 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 A143501.
%F A384581 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(3*n-3*j+k,j)/(3*n-3*j+k) * A(n-j,j).
%e A384581 Square array begins:
%e A384581 1, 1, 1, 1, 1, 1, 1, ...
%e A384581 0, 1, 2, 3, 4, 5, 6, ...
%e A384581 0, 1, 3, 6, 10, 15, 21, ...
%e A384581 0, 4, 10, 19, 32, 50, 74, ...
%e A384581 0, 16, 41, 78, 131, 205, 306, ...
%e A384581 0, 92, 224, 411, 672, 1031, 1518, ...
%e A384581 0, 616, 1464, 2617, 4170, 6245, 8997, ...
%o A384581 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-3*j+k, j)/(3*n-3*j+k)*a(n-j, j)));
%Y A384581 Columns k=0..1 give A000007, A143501.
%Y A384581 Cf. A381566, A384580, A384582, A384583.
%K A384581 nonn,tabl
%O A384581 0,8
%A A384581 _Seiichi Manyama_, Jun 04 2025