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

0,3

Comments

Refer to comments in A174713.

Row sums = A000041, the partition numbers.

Links

Table of n, a(n) for n=0..44.

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.

Example

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.

Sequence in context: A325612 A054995 A018219 * A116633 A263232 A134666

Adjacent sequences: A174711 A174712 A174713 * A174715 A174716 A174717

Keyword

nonn,tabf

Author

Gary W. Adamson, Mar 27 2010

Status

approved