%I #5 Oct 30 2012 00:54:59
%S 1,0,1,1,0,1,3,1,0,2,14,3,1,0,6,77,14,3,2,0,24,497,77,14,6,6,0,120,
%T 3676,497,77,28,18,24,0,720,30677,3676,497,154,84,72,120,0,5040,
%U 285335,30677,3676,994,462,336,360,720,0,40320
%N Eigentriangle based on A052186 (permutations without strong fixed points), row sums = n!
%C Row sums = n!. Sum n-th row terms = rightmost term of next row.
%C Left border = A052186.
%F Eigentriangle by rows, T(n,k) = A052186(n-k)*X; 0<=k<=n; where X = an infinite lower triangular matrix with the factorials shifted to (1, 1, 1, 2, 6, 24,...) in the main diagonal and the rest zeros. The triangle A052186 is composed of A052186 in every column: (1, 0, 1, 3, 14, 77, 497,...). The operations are equivalent to (by rows): termwise products of (n+1) terms of A052186 (reversed) and an equal number of terms in the series: (1, 1, 1, 2, 6, 24, 120,...).
%e First few rows of the triangle =
%e 1;
%e 0, 1;
%e 1, 0, 1;
%e 3, 1, 0, 2;
%e 14, 3, 1, 0, 6;
%e 77, 14, 3, 2, 0, 24;
%e 497, 77, 14, 6, 6, 0, 120;
%e 3676, 497, 77, 28, 18, 24, 0, 720;
%e 30677, 3676, 497, 154, 84, 72, 120, 0, 5040;
%e 285335, 30677, 3676, 994, 462, 336, 360, 720, 0, 40320;
%e ...
%e Row 3 = (14, 3, 1, 0, 6) = termwise products of (14, 3, 1, 0, 1) and (1, 1, 1, 2, 6) = (14*1, 3*1, 1*1, 0*2, 1*6).
%Y A000142, Cf. A052186
%K nonn,tabl
%O 0,7
%A _Gary W. Adamson_, Sep 11 2008
%E Typo in row for n=7 corrected by _Olivier GĂ©rard_, Oct 30 2012