Search: id:A144108
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%I A144108
%S A144108 1,0,1,1,0,1,3,1,0,2,14,3,1,0,6,77,14,3,2,0,24,497,77,14,6,6,0,120,3676,
%T A144108 497,77,28,18,24,0,720,30677,3636,497,154,84,72,120,0,5040,285335,30677,
%U A144108 3676,994,462,336,360,720,0,40320
%N A144108 Eigentriangle, row sums = n!
%C A144108 Row sums = n!. Sum n-th row terms = rightmost term of next row.
%C A144108 Left border = A052186.
%F A144108 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 A144108 First few rows of the triangle =
%e A144108 1;
%e A144108 0, 1;
%e A144108 1, 0, 1;
%e A144108 3, 1, 0, 2;
%e A144108 14, 3, 1, 0, 6;
%e A144108 77, 14, 3, 2, 0, 24;
%e A144108 497, 77, 14, 6, 6, 0, 120;
%e A144108 3676, 497, 77, 28, 18, 24, 0, 720;
%e A144108 30677, 3676, 497, 154, 84, 72, 120, 0, 5040;
%e A144108 285335, 30677, 3676, 994, 462, 336, 360, 720, 0, 40320;
%e A144108 ...
%e A144108 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 A144108 A000142, Cf. A052186
%Y A144108 Sequence in context: A119734 A073200 A104416 this_sequence A163972 A068464 
               A135297
%Y A144108 Adjacent sequences: A144105 A144106 A144107 this_sequence A144109 A144110 
               A144111
%K A144108 nonn,tabl
%O A144108 0,7
%A A144108 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008

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