A340525 Triangle read by rows: T(n,k) = A006218(n-k+1)*A002865(k-1), 1 <= k <= n.

1, 3, 0, 5, 0, 1, 8, 0, 3, 1, 10, 0, 5, 3, 2, 14, 0, 8, 5, 6, 2, 16, 0, 10, 8, 10, 6, 4, 20, 0, 14, 10, 16, 10, 12, 4, 23, 0, 16, 14, 20, 16, 20, 12, 7, 27, 0, 20, 16, 28, 20, 32, 20, 21, 8, 29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12, 35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14

Offset: 1

Author

Omar E. Pol, Jan 10 2021

Keywords

• nonn
• tabl

Comments

Conjecture: the sum of row n equals A006128(n), the total number of parts in all partitions of n.

Examples

			Triangle begins:
   1;
   3,  0;
   5,  0,  1;
   8,  0,  3,  1;
  10,  0,  5,  3,  2;
  14,  0,  8,  5,  6,  2;
  16,  0, 10,  8, 10,  6,  4;
  20,  0, 14, 10, 16, 10, 12,  4;
  23,  0, 16, 14, 20, 16, 20, 12,  7;
  27,  0, 20, 16, 28, 20, 32, 20, 21,  8;
  29,  0, 23, 20, 32, 28, 40, 32, 35, 24, 12;
  35,  0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14;
...
For n = 6 the calculation of every term of row 6 is as follows:
--------------------------
k   A002865         T(6,k)
--------------------------
1      1   *  14   =  14
2      0   *  10   =   0
3      1   *   8   =   8
4      1   *   5   =   5
5      2   *   3   =   6
6      2   *   1   =   2
.           A006218
--------------------------
The sum of row 6 is 14 + 0 + 8 + 5 + 6 + 2 = 35, equaling A006128(6).
		

Crossrefs

Mirror of A245095.

Row sums give A006128 (conjectured).

Columns 1, 3 and 4 are A006218.

Column 2 gives A000004.

Leading diagonal gives A002865.

Cf. A135010, A138121, A221531, A336811, A339106, A340424, A340524, A340426.