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 A384654 #12 Jun 06 2025 08:35:37
%S A384654 1,1,0,1,1,0,1,2,2,0,1,3,5,10,0,1,4,9,24,69,0,1,5,14,43,162,592,0,1,6,
%T A384654 20,68,285,1362,6052,0,1,7,27,100,445,2352,13664,70870,0,1,8,35,140,
%U A384654 650,3612,23171,157592,928497,0,1,9,44,189,909,5201,34972,263190,2039543,13404514,0
%N A384654 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 A384650.
%F A384654 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(5*n-4*j+k,j)/(5*n-4*j+k) * A(n-j,j).
%e A384654 Square array begins:
%e A384654 1, 1, 1, 1, 1, 1, 1, ...
%e A384654 0, 1, 2, 3, 4, 5, 6, ...
%e A384654 0, 2, 5, 9, 14, 20, 27, ...
%e A384654 0, 10, 24, 43, 68, 100, 140, ...
%e A384654 0, 69, 162, 285, 445, 650, 909, ...
%e A384654 0, 592, 1362, 2352, 3612, 5201, 7188, ...
%e A384654 0, 6052, 13664, 23171, 34972 ,49540, 67433, ...
%o A384654 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(5*n-4*j+k, j)/(5*n-4*j+k)*a(n-j, j)));
%Y A384654 Columns k=0..1 give A000007, A384650.
%Y A384654 Cf. A379598, A384651, A384652, A384653.
%K A384654 nonn,tabl
%O A384654 0,8
%A A384654 _Seiichi Manyama_, Jun 06 2025