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 A384718 #11 Jun 08 2025 10:49:53 %S A384718 1,1,0,1,1,0,1,2,5,0,1,3,12,49,0,1,4,21,128,729,0,1,5,32,243,2000, %T A384718 14641,0,1,6,45,400,3993,41472,371293,0,1,7,60,605,6912,85683,1075648, %U A384718 11390625,0,1,8,77,864,10985,153664,2278125,33554432,410338673,0 %N A384718 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 A052750. %F A384718 A(n,k) = k * (2*n+k)^(n-1) for n > 0. %e A384718 Square array begins: %e A384718 1, 1, 1, 1, 1, 1, ... %e A384718 0, 1, 2, 3, 4, 5, ... %e A384718 0, 5, 12, 21, 32, 45, ... %e A384718 0, 49, 128, 243, 400, 605, ... %e A384718 0, 729, 2000, 3993, 6912, 10985, ... %e A384718 0, 14641, 41472, 85683, 153664, 253125, ... %o A384718 (PARI) a(n, k) = if(n==0, 1, k*(2*n+k)^(n-1)); %Y A384718 Columns k=0..2 give A000007, A052750, A097629(n+1). %Y A384718 Cf. A058127, A232006, A384692. %K A384718 nonn,tabl %O A384718 0,8 %A A384718 _Seiichi Manyama_, Jun 08 2025