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 A383818 #25 May 15 2025 08:22:05
%S A383818 1,1,0,1,1,0,1,4,1,0,1,9,10,1,0,1,16,45,22,1,0,1,25,136,177,46,1,0,1,
%T A383818 36,325,856,621,94,1,0,1,49,666,3025,4576,2049,190,1,0,1,64,1225,8646,
%U A383818 23125,22216,6525,382,1,0,1,81,2080,21217,90126,156145,101536,20337,766,1,0
%N A383818 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of 1/(1 - k*x) * Product_{j=0..k-1} (1 + j*x)/(1 - j*x).
%F A383818 A(n,k) = Sum_{j=0..k} |Stirling1(k,j)| * Stirling2(j+n,k).
%e A383818 Square array begins:
%e A383818 1, 1, 1, 1, 1, 1, ...
%e A383818 0, 1, 4, 9, 16, 25, ...
%e A383818 0, 1, 10, 45, 136, 325, ...
%e A383818 0, 1, 22, 177, 856, 3025, ...
%e A383818 0, 1, 46, 621, 4576, 23125, ...
%e A383818 0, 1, 94, 2049, 22216, 156145, ...
%o A383818 (PARI) a(n, k) = sum(j=0, k, abs(stirling(k, j, 1))*stirling(j+n, k, 2));
%Y A383818 Columns k=0..4 give A000007, A000012, A033484, A383912, A383913.
%Y A383818 Main diagonal gives A383839.
%Y A383818 Cf. A287532, A383900.
%K A383818 nonn,tabl
%O A383818 0,8
%A A383818 _Seiichi Manyama_, May 14 2025