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 A383900 #29 May 15 2025 08:22:02
%S A383900 1,1,0,1,2,0,1,6,2,0,1,12,18,2,0,1,20,72,42,2,0,1,30,200,312,90,2,0,1,
%T A383900 42,450,1400,1152,186,2,0,1,56,882,4650,8000,3912,378,2,0,1,72,1568,
%U A383900 12642,38250,40520,12672,762,2,0,1,90,2592,29792,142002,271770,190400,39912,1530,2,0
%N A383900 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of Product_{j=0..k} (1 + j*x)/(1 - j*x).
%F A383900 A(n,k) = Sum_{j=0..k} |Stirling1(k+1,j+1)| * Stirling2(j+n,k).
%e A383900 Square array begins:
%e A383900 1, 1, 1, 1, 1, 1, ...
%e A383900 0, 2, 6, 12, 20, 30, ...
%e A383900 0, 2, 18, 72, 200, 450, ...
%e A383900 0, 2, 42, 312, 1400, 4650, ...
%e A383900 0, 2, 90, 1152, 8000, 38250, ...
%e A383900 0, 2, 186, 3912, 40520, 271770, ...
%o A383900 (PARI) a(n, k) = sum(j=0, k, abs(stirling(k+1, j+1, 1))*stirling(j+n, k, 2));
%Y A383900 Columns k=0..4 give A000007, A040000, A068293(n+1), A383910, A383911.
%Y A383900 Main diagonal gives A350366.
%Y A383900 A(n,n-1) gives A383767.
%Y A383900 Cf. A383818, A383843.
%K A383900 nonn,tabl
%O A383900 0,5
%A A383900 _Seiichi Manyama_, May 14 2025