%I A089258
%S A089258 1,1,0,1,1,1,1,2,2,2,1,3,5,6,9,1,4,10,16,24,44,1,5,17,38,65,120,265,1,
               6,
%T A089258 26,78,168,326,720,1854,1,7,37,142,393,872,1957,5040,14833,1,8,50,236,
%U A089258 824,2208,5296,13700,40320,133496
%N A089258 Another version of A080955.
%F A089258 For n>0, T(n, k) is the permanent of the n X n matrix with k on the diagonal 
               and 1 elsewhere; T(0, k) = 1. T(n, k) = Sum(j>=0; A008290(n, j)*k^j). 
               T(n, k) = n*T(n-1, k) + (k-1)^n . T(n, k) = n!*Sum(j=0..n; (k-1)^j/
               j! ) For column k, E.g.f. : exp((k-1)*x/(1-x)).
%e A089258 Row n=0: 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A089258 Row n=1: 0, 1, 2, 3, 4, 5, 6, 7, ...
%e A089258 Row n=2: 1, 2, 5, 10, 17, 26, 37, ...
%e A089258 Row n=3: 2, 6, 16, 38, 78, 152, 236, ...
%e A089258 Row n=4: 9, 24, 65, 168, 393, 824, ...
%Y A089258 Columns give : A000166 A000142 A000522 A010852 A053486 A053487 A080954
%Y A089258 Cf. A080955 A008290.
%Y A089258 Sequence in context: A055253 A103626 A026268 this_sequence A004065 A127496 
               A144393
%Y A089258 Adjacent sequences: A089255 A089256 A089257 this_sequence A089259 A089260 
               A089261
%K A089258 easy,nonn,tabl
%O A089258 0,8
%A A089258 DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 12 2003