A143228 Triangle read by rows, T(n,k) = (p(n)*p(k)), where p(n) & p(k) = the number of partitions of n; 0<=k<=n.

1, 1, 1, 2, 2, 4, 3, 3, 6, 9, 5, 5, 10, 15, 25, 7, 7, 1421, 35, 49, 11, 11, 22, 33, 55, 77, 121, 15, 15, 30, 45, 75, 105, 165, 225, 22, 22, 44, 66, 110, 154, 242, 330, 484, 30, 30, 60, 90, 150, 210, 330, 450, 660, 900, 42, 42, 84, 126, 210, 294, 462630, 924, 1260, 1764

Offset

0,4

Comments

Left border = A000041.

Row sums = A143229: (1, 2, 8, 21, 60, 133, 330, 675,...).

Links

Table of n, a(n) for n=0..63.

Formula

Triangle read by rows, T(n,k) = (p(n)*p(k)), where p(n) & p(k) = the number of partitions of n. Let X = the infinite lower triangular matrix with A000041 in the main diagonal and the rest zeros = A000041 * 0^(n-k); 0<=k<=n. The triangle = X * A000012 * X.

Example

First few rows of the triangle =
1;
1, 1;
2, 2, 4;
3, 3, 6, 9;
5, 5, 10, 15, 25;
7, 7, 14, 21, 35, 49;
11, 11, 22, 33, 55, 77, 121;
15, 15, 30, 45, 75, 105, 165, 225;
...
T(7,4) = 75 = p(7) * p(4) = 15 * 5.

Crossrefs

Cf. A000041, A143229.

Sequence in context: A303691 A205678 A128590 * A143211 A361757 A209755

Adjacent sequences: A143225 A143226 A143227 * A143229 A143230 A143231

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 31 2008

Status

approved