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A174714 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.

%I A174714 #8 Jan 31 2013 04:30:43
%S A174714 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 A174714 16,14,6,5,44,22,18,12,5,57,27,26,15,10
%N A174714 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 A174714 Refer to comments in A174713.
%C A174714 Row sums = A000041, the partition numbers.
%F A174714 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 A174714 First few rows of the triangle =
%e A174714 1;
%e A174714 1;
%e A174714 2;
%e A174714 2, 1;
%e A174714 4, 1;
%e A174714 5, 2;
%e A174714 7, 2, 2;
%e A174714 9, 4, 2;
%e A174714 13, 5, 4;
%e A174714 16, 7, 4, 3;
%e A174714 22, 9, 8, 3;
%e A174714 27, 13, 10, 6;
%e A174714 36, 16, 14, 6, 5;
%e A174714 44, 22, 18, 12, 5;
%e A174714 57, 27, 26, 15, 10;
%e A174714 ...
%Y A174714 Cf. A000041, A000726, A174712, A174713, A174715.
%K A174714 nonn,tabf
%O A174714 0,3
%A A174714 _Gary W. Adamson_, Mar 27 2010