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 A379168 #20 Feb 27 2025 11:17:23 %S A379168 1,1,0,1,1,0,1,2,5,0,1,3,12,55,0,1,4,21,140,1005,0,1,5,32,261,2600, %T A379168 26601,0,1,6,45,424,4965,68752,941863,0,1,7,60,635,8304,132003, %U A379168 2414188,42372177,0,1,8,77,900,12845,223104,4617675,107385896,2336926665,0 %N A379168 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A140049. %F A379168 See A140049. %e A379168 Square array begins: %e A379168 1, 1, 1, 1, 1, 1, 1, ... %e A379168 0, 1, 2, 3, 4, 5, 6, ... %e A379168 0, 5, 12, 21, 32, 45, 60, ... %e A379168 0, 55, 140, 261, 424, 635, 900, ... %e A379168 0, 1005, 2600, 4965, 8304, 12845, 18840, ... %e A379168 0, 26601, 68752, 132003, 223104, 350125, 522576, ... %e A379168 0, 941863, 2414188, 4617675, 7806424, 12296935, 18477828, ... %o A379168 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n+k)^(j-1)*binomial(n, j)*a(n-j, j))); %Y A379168 Columns k=0..1 give A000007, A140049. %Y A379168 Cf. A058127, A380178. %K A379168 nonn,tabl %O A379168 0,8 %A A379168 _Seiichi Manyama_, Feb 11 2025