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 A384621 #11 Jun 05 2025 09:55:26
%S A384621 1,1,0,1,1,0,1,2,6,0,1,3,13,55,0,1,4,21,122,622,0,1,5,30,202,1390,
%T A384621 8015,0,1,6,40,296,2322,17934,113164,0,1,7,51,405,3437,30030,252847,
%U A384621 1711898,0,1,8,63,530,4755,44600,423111,3814724,27357970,0,1,9,76,672,6297,61966,628454,6369930,60766238,457507917,0
%N A384621 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 A376176.
%F A384621 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(n+j+k,j)/(n+j+k) * A(n-j,4*j).
%e A384621 Square array begins:
%e A384621 1, 1, 1, 1, 1, 1, 1, ...
%e A384621 0, 1, 2, 3, 4, 5, 6, ...
%e A384621 0, 6, 13, 21, 30, 40, 51, ...
%e A384621 0, 55, 122, 202, 296, 405, 530, ...
%e A384621 0, 622, 1390, 2322, 3437, 4755, 6297, ...
%e A384621 0, 8015, 17934, 30030, 44600, 61966, 82476, ...
%e A384621 0, 113164, 252847, 423111, 628454, 873840, 1164730, ...
%o A384621 (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, 4*j)));
%Y A384621 Columns k=0..1 give A000007, A376176(n+1).
%Y A384621 Cf. A379599, A384619, A384620, A384623.
%K A384621 nonn,tabl
%O A384621 0,8
%A A384621 _Seiichi Manyama_, Jun 05 2025