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 A384619 #12 Jun 05 2025 09:55:37
%S A384619 1,1,0,1,1,0,1,2,4,0,1,3,9,24,0,1,4,15,56,178,0,1,5,22,97,420,1512,0,
%T A384619 1,6,30,148,738,3572,14152,0,1,7,39,210,1145,6300,33328,142705,0,1,8,
%U A384619 49,284,1655,9832,58702,334354,1528212,0,1,9,60,371,2283,14321,91640,586635,3559310,17211564,0
%N A384619 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of (B(x)/x)^k, where B(x) is the g.f. of A213591.
%F A384619 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(n+j+k,j)/(n+j+k) * A(n-j,2*j).
%e A384619 Square array begins:
%e A384619 1, 1, 1, 1, 1, 1, 1, ...
%e A384619 0, 1, 2, 3, 4, 5, 6, ...
%e A384619 0, 4, 9, 15, 22, 30, 39, ...
%e A384619 0, 24, 56, 97, 148, 210, 284, ...
%e A384619 0, 178, 420, 738, 1145, 1655, 2283, ...
%e A384619 0, 1512, 3572, 6300, 9832, 14321, 19938, ...
%e A384619 0, 14152, 33328, 58702, 91640, 133720, 186753, ...
%o A384619 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+j+k, j)/(n+j+k)*a(n-j, 2*j)));
%Y A384619 Columns k=0..1 give A000007, A213591(n+1).
%Y A384619 Cf. A379599, A384620, A384621, A384623.
%K A384619 nonn,tabl
%O A384619 0,8
%A A384619 _Seiichi Manyama_, Jun 04 2025