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 A089225 #4 Feb 22 2013 14:38:50
%S A089225 1,2,1,7,4,3,35,22,17,14,228,154,122,102,88,1834,1310,1060,898,782,
%T A089225 694,17582,13128,10818,9272,8142,7272,6578,195866,151560,126882,
%U A089225 109880,97218,87336,79370,72792,2487832,1981824,1682196,1470304,1309776
%N A089225 Triangle T(n,k) read by rows, defined by T(n,k) = (n-k)*T(n-1,k)+Sum(k=1..n, T(n-1,k)); T(1,1) = 1, T(1,k)= 0 if k >1.
%C A089225 Let M be the n X n matrix with M(i,i)=i, other entries 1. Then T(n,k) = permanent of n-1 X n-1 matrix obtained by omitting row k and column k from M.
%C A089225 T(n,1) = A003713(n). n-th row sum = T(n+1,n+1) = A007840(n). {1}, {2, 1}, {7, 4, 3}, {35, 22, 17, 14}, ...
%e A089225 n=4: M = |1,1,1,1|1, 2,1, 1|1, 1, 3, 1|1, 1, 1, 4|
%e A089225 T(4, 1) = permanent of |2, 1, 1|1, 3, 1|1, 1, 4| = 26+5+4 = 35
%e A089225 T(4, 2) = permanent of |1, 1, 1|1, 3, 1|1, 1, 4| = 13+5+4 = 22
%e A089225 T(4, 3) = permanent of |1, 1, 1|1, 2, 1|1, 1, 4| = 9+5+3 = 17
%e A089225 T(4, 4) = permanent of |1, 1, 1|1, 2, 1|1, 1, 3| = 7+4+3 = 14
%K A089225 easy,nonn,tabl
%O A089225 1,2
%A A089225 _Philippe Deléham_, Dec 10 2003