A179313 -id:A179313 - cp's OEIS frontend

A179315 Nonzero differences A179313(n,k)- A127742(n,k) read along rows.

1, 8, 2, 50, 16, 2, 3, 294, 100, 16, 4, 24, 6, 4, 1717, 588, 100, 32, 11, 150, 48, 12, 3, 32, 12, 5, 10194, 3434, 588, 200, 124, 882, 300

Offset: 4

Alford Arnold, Jul 12 2010

Refinement of the nonzero entries of A016098.

			A179313 .begins 1; 1 1; 2 2 1; 6 4 1 3 1; 22 12 4 6 3 4 1; 92 44 12 18
A127742 .begins 1; 1 1; 2 2 1; 5 4 1 3 1; 14 10 4 6 3 4 1; 42 28 10 15
so
This seq begins................1...........8..2............50 16 02 03

Cf. A000041, A016098, A000110, A000108, A179313

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

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.

Original entry on oeis.org

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

Alford Arnold, Jul 12 2010

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

			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;

Cf. A000041, A179379, A074664.

A048996(n,k)* T(n,k) = A179313(n,k).
sum_{k=1.. A000041(n)} T(n,k) = A179379(n).
T(n,1) = A074664(n).

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

cp's OEIS Frontend

A179315 Nonzero differences A179313(n,k)- A127742(n,k) read along rows.

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