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.

1, 2, 1, 7, 4, 3, 35, 22, 17, 14, 228, 154, 122, 102, 88, 1834, 1310, 1060, 898, 782, 694, 17582, 13128, 10818, 9272, 8142, 7272, 6578, 195866, 151560, 126882, 109880, 97218, 87336, 79370, 72792, 2487832, 1981824, 1682196, 1470304, 1309776

Offset: 1

Author

Philippe Deléham, Dec 10 2003

Keywords

• easy
• nonn
• tabl

Comments

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.

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}, ...

Examples

			n=4: M = |1,1,1,1|1, 2,1, 1|1, 1, 3, 1|1, 1, 1, 4|
T(4, 1) = permanent of |2, 1, 1|1, 3, 1|1, 1, 4| = 26+5+4 = 35
T(4, 2) = permanent of |1, 1, 1|1, 3, 1|1, 1, 4| = 13+5+4 = 22
T(4, 3) = permanent of |1, 1, 1|1, 2, 1|1, 1, 4| = 9+5+3 = 17
T(4, 4) = permanent of |1, 1, 1|1, 2, 1|1, 1, 3| = 7+4+3 = 14