A340426 Triangle read by rows: T(n,k) = A000203(n-k+1)*A002865(k-1), 1 <= k <= n.

1, 3, 0, 4, 0, 1, 7, 0, 3, 1, 6, 0, 4, 3, 2, 12, 0, 7, 4, 6, 2, 8, 0, 6, 7, 8, 6, 4, 15, 0, 12, 6, 14, 8, 12, 4, 13, 0, 8, 12, 12, 14, 16, 12, 7, 18, 0, 15, 8, 24, 12, 28, 16, 21, 8, 12, 0, 13, 15, 16, 24, 14, 28, 28, 24, 12, 28, 0, 18, 13, 30, 16, 48, 24, 49, 32, 36, 14, 14, 0, 12

Offset: 1

Author

Omar E. Pol, Jan 07 2021

Keywords

• nonn
• tabl

Comments

Conjecture: the sum of row n equals A138879(n), the sum of all parts in the last section of the set of partitions of n.

Examples

			Triangle begins:
   1;
   3,  0;
   4,  0,  1;
   7,  0,  3,  1;
   6,  0,  4,  3,  2;
  12,  0,  7,  4,  6,  2;
   8,  0,  6,  7,  8,  6,  4;
  15,  0, 12,  6, 14,  8, 12,  4;
  13,  0,  8, 12, 12, 14, 16, 12,  7;
  18,  0, 15,  8, 24, 12, 28, 16, 21,  8;
  12,  0, 13, 15, 16, 24, 14, 28, 28, 24, 12;
  28,  0, 18, 13, 30, 16, 48, 24, 49, 32, 36, 14;
...
For n = 6 the calculation of every term of row 6 is as follows:
--------------------------
k   A002865         T(6,k)
--------------------------
1      1   *   12  =  12
2      0   *   6   =   0
3      1   *   7   =   7
4      1   *   4   =   4
5      2   *   3   =   6
6      2   *   1   =   2
.           A000203
--------------------------
The sum of row 6 is 12 + 0 + 7 + 4 + 6 + 2 = 31, equaling A138879(6) = 31.
		

Crossrefs

Columns 1, 3 and 4 give A000203.

Column 2 gives A000004.

Columns 5 and 6 gives A074400.

Column 7 and 8 give A239050.

Column 9 gives A319527.

Column 10 gives A319528.

Leading diagonal gives A002865.

Cf. A135010, A138879.