A283417 Number T(n,k) of triangle-free graphs on n unlabeled nodes with exactly k connected components; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 3, 2, 1, 1, 0, 6, 4, 2, 1, 1, 0, 19, 10, 5, 2, 1, 1, 0, 59, 28, 11, 5, 2, 1, 1, 0, 267, 90, 32, 12, 5, 2, 1, 1, 0, 1380, 363, 100, 33, 12, 5, 2, 1, 1, 0, 9832, 1784, 397, 104, 34, 12, 5, 2, 1, 1, 0, 90842, 11770, 1892, 407, 105, 34, 12, 5, 2, 1, 1

Offset

0,12

Links

Alois P. Heinz, Rows n = 0..17, flattened

Index entries for triangles generated by the Multiset Transformation

Formula

G.f.: Product_{j>=1} 1/(1-y*x^j)^A024607(j).

Example

Triangle T(n,k) begins:
  1;
  0,    1;
  0,    1,    1;
  0,    1,    1,   1;
  0,    3,    2,   1,   1;
  0,    6,    4,   2,   1,  1;
  0,   19,   10,   5,   2,  1,  1;
  0,   59,   28,  11,   5,  2,  1, 1;
  0,  267,   90,  32,  12,  5,  2, 1, 1;
  0, 1380,  363, 100,  33, 12,  5, 2, 1, 1;
  0, 9832, 1784, 397, 104, 34, 12, 5, 2, 1, 1;
  ...

Crossrefs

Columns k=0-1 give: A000007, A024607.

Row sums give A006785.

Sequence in context: A287576 A035103 A155033 * A107889 A138384 A129172

Adjacent sequences: A283414 A283415 A283416 * A283418 A283419 A283420

Keyword

nonn,tabl

Author

Alois P. Heinz, Apr 14 2017

Status

approved