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 A256895 #6 Apr 29 2015 06:39:00
%S A256895 1,1,1,1,3,1,1,11,7,1,1,49,47,13,1,1,261,341,139,21,1,1,1631,2731,
%T A256895 1471,329,31,1,1,11743,24173,16213,4789,671,43,1,1,95901,235463,
%U A256895 189373,69441,12881,1231,57,1,1,876809,2509621,2357503,1032245,237961,30169,2087,73,1
%N A256895 Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} j!*C(n-1,j-1)*T(n-j,k-1) if k != 0 else 1, n>=0, 0<=k<=n.
%C A256895 Can be understood as a convolution matrix or as a sequence-to-triangle transformation similar to the partial Bell polynomials defined as: S -> T(n, k, S) = Sum_{j=0..n-k+1} C(n-1,j-1)*S(j)*T(n-j,k-1,S) if k != 0 else S(0)^n. Here S(n) = n!. The case S(n) = n gives the triangle of idempotent numbers A059297 and the case S(n) = 1 for all n leads to A256894.
%F A256895 T(n+1,1) = A001339(n) for n>=0.
%F A256895 T(n,n-1) = A002061(n) for n>=1.
%e A256895 Triangle starts:
%e A256895 1;
%e A256895 1, 1;
%e A256895 1, 3, 1;
%e A256895 1, 11, 7, 1;
%e A256895 1, 49, 47, 13, 1;
%e A256895 1, 261, 341, 139, 21, 1;
%p A256895 # Implemented as a sequence transformation acting on f: n -> n!.
%p A256895 F := proc(n, k, f) option remember; `if`(k=0, f(0)^n,
%p A256895 add(binomial(n-1, j-1)*f(j)*F(n-j, k-1, f), j=0..n-k+1)) end:
%p A256895 for n from 0 to 7 do seq(F(n, k, j->j!), k=0..n) od;
%Y A256895 Cf. A001339, A002061, A059297, A256894.
%K A256895 nonn,tabl,easy
%O A256895 0,5
%A A256895 _Peter Luschny_, Apr 28 2015