A255768 Triangle read by rows: T(n,k) = total number of parts in all partitions of n into k distinct parts.

1, 3, 4, 2, 7, 5, 6, 14, 12, 20, 3, 8, 39, 7, 15, 52, 19, 13, 74, 41, 18, 102, 68, 4, 12, 134, 120, 9, 28, 158, 189, 24, 14, 208, 283, 51, 24, 259, 390, 107, 24, 284, 582, 173, 5, 31, 361, 749, 311, 11, 18, 409, 1024, 485, 29, 39, 488, 1289, 767, 61

Offset: 1

Author

Omar E. Pol, May 21 2015

Keywords

• nonn
• tabf
• look

Comments

Column 1 is sigma = A000203.

Column 2 is A216669.

Row sums give A006128.

Row n has length A003056(n) hence the first element of column k is in row A000217(n).

The first positive element in column k is k.

Examples

			Triangle begins:
   1;
   3;
   4,   2;
   7,   5;
   6,  14;
  12,  20,    3;
   8,  39,    7;
  15,  52,   19;
  13,  74,   41;
  18, 102,   68,    4;
  12, 134,  120,    9;
  28, 158,  189,   24;
  14, 208,  283,   51;
  24, 259,  390,  107;
  24, 284,  582,  173,   5;
  31, 361,  749,  311,  11;
  18, 409, 1024,  485,  29;
  39, 488, 1289,  767,  61;
  20, 538, 1699, 1114, 127;
  42, 634, 2092, 1624, 238;
  32, 678, 2642, 2291, 403, 6;
  ...
		

Links

• Alois P. Heinz, Rows n = 1..500, flattened

Crossrefs

Cf. A000041, A000203, A000217, A006128, A003056, A116608, A216669, A255767.

Formula

T(n,1) = A000203(n).

Extensions

a(27) and beyond from Alois P. Heinz, Jul 26 2015