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 A254883 #8 Feb 10 2015 11:35:06
%S A254883 1,0,1,0,1,1,0,2,2,1,0,6,9,3,1,0,24,48,24,4,1,0,120,300,200,50,5,1,0,
%T A254883 720,2160,1800,600,90,6,1,0,5040,17640,17640,7350,1470,147,7,1,0,
%U A254883 40320,161280,188160,94080,23520,3136,224,8,1
%N A254883 Triangle read by rows, T(n,k) = sum(j=0..2*(n-k), A254882(n-k,j)*k^j /(n-k)!), n>=0, 0<=k<=n.
%e A254883 [1]
%e A254883 [0, 1]
%e A254883 [0, 1, 1]
%e A254883 [0, 2, 2, 1]
%e A254883 [0, 6, 9, 3, 1]
%e A254883 [0, 24, 48, 24, 4, 1]
%e A254883 [0, 120, 300, 200, 50, 5, 1]
%e A254883 [0, 720, 2160, 1800, 600, 90, 6, 1]
%t A254883 Flatten[{1,0,1,Table[{0,Table[Sum[Sum[Abs[StirlingS1[n-k,m+1]] * Abs[StirlingS1[n-k,j-m]],{m,0,j-1}]*k^j/(n-k)!,{j,0,2*(n-k)}],{k,1,n-1}],1},{n,2,10}]}] (* _Vaclav Kotesovec_, Feb 10 2015 *)
%o A254883 (Sage)
%o A254883 T = lambda n,k: sum(A254882(n-k,j)*k^j/factorial(n-k) for j in (0..2*(n-k)))
%o A254883 for n in range(6): [T(n,k) for k in (0..n)]
%Y A254883 Cf. A254882.
%K A254883 nonn,tabl
%O A254883 0,8
%A A254883 _Peter Luschny_, Feb 10 2015