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 A384653 #11 Jun 06 2025 08:35:48
%S A384653 1,1,0,1,1,0,1,2,2,0,1,3,5,9,0,1,4,9,22,56,0,1,5,14,40,134,432,0,1,6,
%T A384653 20,64,240,1012,3935,0,1,7,27,95,381,1779,9039,40820,0,1,8,35,134,565,
%U A384653 2780,15596,92246,471633,0,1,9,44,182,801,4071,23950,156597,1051558,5980210,0
%N A384653 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 A384649.
%F A384653 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(4*n-3*j+k,j)/(4*n-3*j+k) * A(n-j,j).
%e A384653 Square array begins:
%e A384653 1, 1, 1, 1, 1, 1, 1, ...
%e A384653 0, 1, 2, 3, 4, 5, 6, ...
%e A384653 0, 2, 5, 9, 14, 20, 27, ...
%e A384653 0, 9, 22, 40, 64, 95, 134, ...
%e A384653 0, 56, 134, 240, 381, 565, 801, ...
%e A384653 0, 432, 1012, 1779, 2780, 4071, 5718, ...
%e A384653 0, 3935, 9039, 15596, 23950, 34515, 47786, ...
%o A384653 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(4*n-3*j+k, j)/(4*n-3*j+k)*a(n-j, j)));
%Y A384653 Columns k=0..1 give A000007, A384649.
%Y A384653 Cf. A379598, A384651, A384652, A384654.
%K A384653 nonn,tabl
%O A384653 0,8
%A A384653 _Seiichi Manyama_, Jun 06 2025