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 A384620 #11 Jun 05 2025 09:55:30
%S A384620 1,1,0,1,1,0,1,2,5,0,1,3,11,38,0,1,4,18,86,357,0,1,5,26,145,815,3832,
%T A384620 0,1,6,35,216,1389,8758,45189,0,1,7,45,300,2095,14967,103056,572378,0,
%U A384620 1,8,56,398,2950,22668,175937,1300586,7676653,0,1,9,68,511,3972,32091,266470,2214012,17368633,107971691,0
%N A384620 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 A213639.
%F A384620 A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(n+j+k,j)/(n+j+k) * A(n-j,3*j).
%e A384620 Square array begins:
%e A384620 1, 1, 1, 1, 1, 1, 1, ...
%e A384620 0, 1, 2, 3, 4, 5, 6, ...
%e A384620 0, 5, 11, 18, 26, 35, 45, ...
%e A384620 0, 38, 86, 145, 216, 300, 398, ...
%e A384620 0, 357, 815, 1389, 2095, 2950, 3972, ...
%e A384620 0, 3832, 8758, 14967, 22668, 32091, 43488, ...
%e A384620 0, 45189, 103056, 175937, 266470, 377620, 512705, ...
%o A384620 (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, 3*j)));
%Y A384620 Columns k=0..1 give A000007, A213639(n+1).
%Y A384620 Cf. A379599, A384619, A384621, A384623.
%K A384620 nonn,tabl
%O A384620 0,8
%A A384620 _Seiichi Manyama_, Jun 05 2025