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

1,4

Comments

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

Links

Table of n, a(n) for n=1..81.

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).

Example

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.

Sequence in context: A125731 A123361 A265315 * A107106 A178249 A119502

Adjacent sequences: A179377 A179378 A179379 * A179381 A179382 A179383

Keyword

nonn,tabf

Author

Alford Arnold, Jul 12 2010

Extensions

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

Status

approved