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 A384651 #11 Jun 06 2025 08:35:41
%S A384651 1,1,0,1,1,0,1,2,2,0,1,3,5,7,0,1,4,9,18,33,0,1,5,14,34,84,189,0,1,6,
%T A384651 20,56,159,472,1249,0,1,7,27,85,265,882,3057,9237,0,1,8,35,122,410,
%U A384651 1460,5615,22190,74972,0,1,9,44,168,603,2256,9166,40053,177149,659042,0
%N A384651 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 A162661.
%F A384651 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(2*n-j+k,j)/(2*n-j+k) * A(n-j,j).
%e A384651 Square array begins:
%e A384651 1, 1, 1, 1, 1, 1, 1, ...
%e A384651 0, 1, 2, 3, 4, 5, 6, ...
%e A384651 0, 2, 5, 9, 14, 20, 27, ...
%e A384651 0, 7, 18, 34, 56, 85, 122, ...
%e A384651 0, 33, 84, 159, 265, 410, 603, ...
%e A384651 0, 189, 472, 882, 1460, 2256, 3330, ...
%e A384651 0, 1249, 3057, 5615, 9166, 14015, 20540, ...
%o A384651 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-j+k, j)/(2*n-j+k)*a(n-j, j)));
%Y A384651 Columns k=0..1 give A000007, A162661.
%Y A384651 Cf. A379598, A384652, A384653, A384654.
%K A384651 nonn,tabl
%O A384651 0,8
%A A384651 _Seiichi Manyama_, Jun 06 2025