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 A379598 #19 Feb 27 2025 11:17:19 %S A379598 1,1,0,1,1,0,1,2,2,0,1,3,5,6,0,1,4,9,16,23,0,1,5,14,31,62,104,0,1,6, %T A379598 20,52,123,278,531,0,1,7,27,80,213,552,1398,2982,0,1,8,35,116,340,964, %U A379598 2750,7718,18109,0,1,9,44,161,513,1561,4784,14976,46083,117545,0 %N A379598 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 A110447. %F A379598 See A030266. %e A379598 Square array begins: %e A379598 1, 1, 1, 1, 1, 1, 1, ... %e A379598 0, 1, 2, 3, 4, 5, 6, ... %e A379598 0, 2, 5, 9, 14, 20, 27, ... %e A379598 0, 6, 16, 31, 52, 80, 116, ... %e A379598 0, 23, 62, 123, 213, 340, 513, ... %e A379598 0, 104, 278, 552, 964, 1561, 2400, ... %e A379598 0, 531, 1398, 2750, 4784, 7755, 11987, ... %o A379598 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+k, j)/(n+k)*a(n-j, j))); %Y A379598 Columns k=0..1 give A000007, A110447 (A030266(n+1)). %Y A379598 Cf. A379599, A380178. %K A379598 nonn,tabl %O A379598 0,8 %A A379598 _Seiichi Manyama_, Feb 27 2025