%I A144107
%S A144107 1,1,1,3,1,2,13,3,2,6,71,13,6,6,24,461,71,26,18,24,120,3447,461,142,78,
%T A144107 72,120,720,29093,3447,922,426,312,360,720,5040
%N A144107 Eigentriangle, row sums = n!
%C A144107 Sum of n-th row terms = rightmost term of next row.
%C A144107 Left border = A003319.
%F A144107 Eigentriangle by rows, T(n,k) = A003319(n-k+1)*((n-1)!).
%F A144107 Given an infinite lower triangular matrix with A003319 in every column: 
               (1, 1, 3, 13, 71,...); we apply termwise products of row terms to 
               an equal number of
%F A144107 terms in the factorial sequence: (1, 1, 2, 6, 24,...).
%e A144107 First few rows of the triangle =
%e A144107 1;
%e A144107 1, 1;
%e A144107 3, 1, 2;
%e A144107 13, 3, 2, 6;
%e A144107 71, 13, 6, 6, 24;
%e A144107 461, 71, 26, 18, 24, 120;
%e A144107 3447, 461, 142, 78, 72, 120, 720;
%e A144107 29093, 3447, 922, 426, 312, 360, 720, 5040;
%e A144107 ...
%e A144107 Example: Row 4 = (13, 3, 2, 6) = termwise products of (13, 3, 1, 1) and 
               (1, 1, 2, 6) = (13*1, 3*1, 1*2, 1*6); where (13, 3, 1, 1) = the first 
               4 terms of A003319, reversed. [Line corrected by Brad Fox, Sep 15 
               2008]
%Y A144107 Cf. A000142, A003319.
%Y A144107 Sequence in context: A092580 A004468 A145463 this_sequence A163485 A126038 
               A088363
%Y A144107 Adjacent sequences: A144104 A144105 A144106 this_sequence A144108 A144109 
               A144110
%K A144107 nonn,tabl
%O A144107 1,4
%A A144107 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008