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

1,2

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.

Links

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

Formula

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

Example

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;
  ...

Crossrefs

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

Sequence in context: A378523 A205769 A166108 * A216221 A296431 A045901

Adjacent sequences: A255765 A255766 A255767 * A255769 A255770 A255771

Keyword

nonn,tabf,look

Author

Omar E. Pol, May 21 2015

Extensions

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

Status

approved