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 A380178 #68 Feb 27 2025 11:17:15 %S A380178 1,1,0,1,1,0,1,2,3,0,1,3,8,22,0,1,4,15,62,281,0,1,5,24,126,792,5396,0, %T A380178 1,6,35,220,1641,14922,142297,0,1,7,48,350,2960,30708,384316,4865806, %U A380178 0,1,8,63,522,4905,55604,777537,12836406,207407489,0,1,9,80,742,7656,93300,1393720,25450806,535396784,10710044776,0 %N A380178 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 A162659. %F A380178 See A162659. %e A380178 Square array begins: %e A380178 1, 1, 1, 1, 1, 1, 1, ... %e A380178 0, 1, 2, 3, 4, 5, 6, ... %e A380178 0, 3, 8, 15, 24, 35, 48, ... %e A380178 0, 22, 62, 126, 220, 350, 522, ... %e A380178 0, 281, 792, 1641, 2960, 4905, 7656, ... %e A380178 0, 5396, 14922, 30708, 55604, 93300, 148446, ... %e A380178 0, 142297, 384316, 777537, 1393720, 2330305, 3716532, ... %o A380178 (PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, j))); %Y A380178 Columns k=0..1 give A000007, A162659. %Y A380178 Cf. A379168. %K A380178 nonn,tabl %O A380178 0,8 %A A380178 _Seiichi Manyama_, Feb 11 2025