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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 8 07:58 EST 2021. Contains 341941 sequences. (Running on oeis4.)