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A180264 Triangle, row sums = A006054; derived from an infinite lower triangular matrix with (1,1,1,...) as the leftmost column and (1,2,1,1,1,...) as other columns.

%I A180264 #2 Mar 30 2012 17:25:39
%S A180264 1,1,1,2,2,1,1,1,4,5,1,1,2,10,11,1,1,2,5,22,25,1,1,2,5,11,50,56,1,1,2,
%T A180264 5,11,50,56,1,1,2,5,11,25,112,126,1,1,2,5,11,25,56,252,283,1,1,2,5,11,
%U A180264 25,56,126,566,636,1,1,2,5,11,25,56,126,283,1272,1429
%N A180264 Triangle, row sums = A006054; derived from an infinite lower triangular matrix with (1,1,1,...) as the leftmost column and (1,2,1,1,1,...) as other columns.
%C A180264 Row sums = A006054 starting (1, 2, 5, 11, 25, 56, 126,...).
%C A180264 Sum of n-th row terms = rightmost term of next row.
%F A180264 Let M = an infinite lower triangular matrix with 1's in the leftmost column,
%F A180264 and (1,2,1,1,1,...) as other columns. Let Q = a diagonalized variant of
%F A180264 A006054 (1, 1, 2, 5, 11, 25, 56,...) as the right border and the rest zeros.
%F A180264 Triangle A180264 = M*Q.
%e A180264 First few rows of the triangle =
%e A180264 .
%e A180264 1;
%e A180264 1, 1;
%e A180264 1, 2, 2;
%e A180264 1, 1, 4, 5;
%e A180264 1, 1, 2, 10, 11;
%e A180264 1, 1, 2, 5, 22, 25;
%e A180264 1, 1, 2, 5, 11, 50, 56;
%e A180264 1, 1, 2, 5, 11, 25, 112, 126;
%e A180264 1, 1, 2, 5, 11, 25, 56, 252, 283;
%e A180264 1, 1, 2, 5, 11, 25, 56, 126, 566, 636;
%e A180264 1, 1, 2, 5, 11, 25, 56, 126, 283, 1272, 1429;
%e A180264 1, 1, 2, 5, 11, 25, 56, 126, 283, 636, 2858, 3211;
%e A180264 ...
%e A180264 Example: Row 4 = (1, 1, 4, 5) = termwise products of (1, 1, 2, 1) and (1, 1, 2, 5).
%Y A180264 Cf. A006054
%K A180264 nonn,tabf
%O A180264 1,4
%A A180264 _Gary W. Adamson_, Aug 21 2010