%I #2 Mar 30 2012 17:25:32
%S 1,1,1,3,1,2,13,3,2,6,71,13,6,6,24,461,71,26,18,24,120,3447,461,142,
%T 78,72,120,720,29093,3447,922,426,312,360,720,5040
%N Eigentriangle, row sums = n!
%C Sum of n-th row terms = rightmost term of next row.
%C Left border = A003319.
%F Eigentriangle by rows, T(n,k) = A003319(n-k+1)*((n-1)!).
%F 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 terms in the factorial sequence: (1, 1, 2, 6, 24,...).
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 3, 1, 2;
%e 13, 3, 2, 6;
%e 71, 13, 6, 6, 24;
%e 461, 71, 26, 18, 24, 120;
%e 3447, 461, 142, 78, 72, 120, 720;
%e 29093, 3447, 922, 426, 312, 360, 720, 5040;
%e ...
%e 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 Cf. A000142, A003319.
%K nonn,tabl
%O 1,4
%A _Gary W. Adamson_, Sep 11 2008