%I #8 Jan 31 2013 04:30:43
%S 1,1,2,2,1,4,1,5,2,7,2,2,9,4,2,13,5,4,16,7,4,3,22,9,8,3,27,13,10,6,36,
%T 16,14,6,5,44,22,18,12,5,57,27,26,15,10
%N Triangle read by rows, Q*M; Q = an infinite lower triangular matrix with A000726 shifted down thrice, M = triangle A174712, the diagonalized variant of A000041.
%C Refer to comments in A174713.
%C Row sums = A000041, the partition numbers.
%F Let Q = an infinite lower triangular matrix with A000726, (Euler transform of [1,1,0,1,1,0,...]) in each column shifted down thrice from the (k-1)-th column, excepting column 0. Let M = triangle A174712, the diagonalized variant of A000041. Then triangle A174714 = Q*M.
%e First few rows of the triangle =
%e 1;
%e 1;
%e 2;
%e 2, 1;
%e 4, 1;
%e 5, 2;
%e 7, 2, 2;
%e 9, 4, 2;
%e 13, 5, 4;
%e 16, 7, 4, 3;
%e 22, 9, 8, 3;
%e 27, 13, 10, 6;
%e 36, 16, 14, 6, 5;
%e 44, 22, 18, 12, 5;
%e 57, 27, 26, 15, 10;
%e ...
%Y Cf. A000041, A000726, A174712, A174713, A174715.
%K nonn,tabf
%O 0,3
%A _Gary W. Adamson_, Mar 27 2010