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 A379599 #18 Feb 27 2025 11:17:27 %S A379599 1,1,0,1,1,0,1,2,3,0,1,3,7,13,0,1,4,12,32,69,0,1,5,18,58,173,419,0,1, %T A379599 6,25,92,321,1054,2809,0,1,7,33,135,523,1971,7039,20353,0,1,8,42,188, %U A379599 790,3248,13158,50632,157199,0,1,9,52,252,1134,4976,21740,94194,387613,1281993,0 %N A379599 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 A088714. %F A379599 See A088714. %e A379599 Square array begins: %e A379599 1, 1, 1, 1, 1, 1, 1, ... %e A379599 0, 1, 2, 3, 4, 5, 6, ... %e A379599 0, 3, 7, 12, 18, 25, 33, ... %e A379599 0, 13, 32, 58, 92, 135, 188, ... %e A379599 0, 69, 173, 321, 523, 790, 1134, ... %e A379599 0, 419, 1054, 1971, 3248, 4976, 7260, ... %e A379599 0, 2809, 7039, 13158, 21740, 33480, 49210, ... %o A379599 (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, j))); %Y A379599 Columns k=0..1 give A000007, A088714. %Y A379599 Cf. A379168, A379598. %K A379599 nonn,tabl %O A379599 0,8 %A A379599 _Seiichi Manyama_, Feb 27 2025