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.

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, 16, 14, 6, 5, 44, 22, 18, 12, 5, 57, 27, 26, 15, 10

Offset: 0

Author

Gary W. Adamson, Mar 27 2010

Keywords

• nonn
• tabf

Comments

Refer to comments in A174713.

Row sums = A000041, the partition numbers.

Examples

			First few rows of the triangle =
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, 16, 14, 6, 5;
44, 22, 18, 12, 5;
57, 27, 26, 15, 10;
...
		

Crossrefs

Cf. A000041, A000726, A174712, A174713, A174715.

Formula

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.