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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.
2
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.
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
KEYWORD
nonn,tabf
AUTHOR
Alford Arnold, Jul 12 2010
EXTENSIONS
Edited and extended by R. J. Mathar, Jul 16 2010
STATUS
approved