A359481 Irregular triangle read by rows in which T(n,k) is one half of the number of overpartitions of n having k distinct parts, n>=1, k>=1.

1, 2, 2, 2, 3, 4, 2, 10, 4, 12, 4, 2, 22, 8, 4, 26, 20, 3, 34, 40, 4, 44, 60, 8, 2, 54, 100, 16, 6, 58, 148, 40, 2, 74, 208, 80, 4, 88, 268, 160, 4, 88, 388, 240, 16, 5, 110, 468, 416, 32, 2, 118, 616, 616, 80, 6, 136, 736, 936, 160, 2, 142, 940, 1296, 320, 6, 162, 1108, 1816, 576

Offset: 1

Author

Omar E. Pol, Mar 31 2023

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1;
  2;
  2,  2;
  3,  4;
  2, 10;
  4, 12,   4;
  2, 22,   8;
  4, 26,  20;
  3, 34,  40;
  4, 44,  60,   8;
  2, 54, 100,  16;
  6, 58, 148,  40;
  2, 74, 208,  80;
  4, 88, 268, 160;
  4, 88, 388, 240, 16;
  ...
		

Crossrefs

Column 1 gives A000005.

Row n has length A003056(n).

Row sums give A014968, n >= 1.

The first element of column k is A000079(k-1).

The first element of column k is in row A000217(k).

Cf. A116608, A235790.

Formula

T(n,k) = (1/2)*A235790(n,k).

T(n,k) = (2^(k-1))*A116608(n,k).