A179380 Triangle T(n,k) read by rows: product of A074664(a_i) of all parts a_i of the k-th partition of n.

1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 1, 22, 6, 2, 2, 1, 1, 1, 92, 22, 6, 4, 6, 2, 1, 2, 1, 1, 1, 426, 92, 22, 12, 22, 6, 4, 2, 6, 2, 1, 2, 1, 1, 1, 2146, 426, 92, 44, 36, 92, 22, 12, 6, 4, 22, 6, 4, 2, 1, 6, 2, 1, 2, 1, 1, 1, 11624, 2146, 426, 184, 132, 426, 92, 44, 36, 22, 12, 8, 92, 22, 12

Offset: 1

Author

Alford Arnold, Jul 12 2010

Keywords

• nonn
• tabf

Comments

Row n has A000041(n) elements, sorted in Abramowitz-Stegun order.

Examples

			T(6,4) refers to the 4th partition of 6, 3+3. T(6,4)=A074664(3)*A074664(3)=2*2.
T(7,3) refers to the 3rd partition of 7, 2+5. T(7,3)=A074664(2)*A074664(5)=1*22.
The triangle starts
1;
1,1;
2,1,1;
6,2,1,1,1;
22,6,2,2,1,1,1;
92,22,6,4,6,2,1,2,1,1,1;
426,92,22,12,22,6,4,2,6,2,1,2,1,1,1;
		

Crossrefs

Cf. A000041, A179379, A074664.

Formula

A048996(n,k)* T(n,k) = A179313(n,k).

sum_{k=1.. A000041(n)} T(n,k) = A179379(n).

T(n,1) = A074664(n).

Extensions

Edited and extended by R. J. Mathar, Jul 16 2010