A193491 Irregular triangle read by rows: row n gives numbers of rooted trees with n nodes (n >= 1) and omega-valency k (k >= 1).

1, 1, 2, 3, 1, 7, 1, 1, 13, 5, 1, 1, 31, 9, 6, 1, 1, 66, 29, 11, 7, 1, 1, 159, 62, 42, 13, 8, 1, 1, 365, 181, 92, 55, 15, 9, 1, 1, 900, 422, 294, 127, 70, 17, 10, 1, 1, 2162, 1166, 720, 435, 165, 86, 19, 11, 1, 1, 5417, 2885, 2119, 1110, 608, 208, 104, 21, 12, 1, 1

Offset

1,3

Comments

See A003120 for definitions.

Links

Table of n, a(n) for n=1..68.

J.-C. Arditti, Dénombrement des arborescences dont le graphe de comparabilité est Hamiltonien, Discrete Math., 5 (1973), 189-200.

Example

Triangle begins:
     1
     1
     2
     3,    1
     7,    1,    1
    13,    5,    1,    1
    31,    9,    6,    1,   1
    66,   29,   11,    7,   1,   1
   159,   62,   42,   13,   8,   1,   1
   365,  181,   92,   55,  15,   9,   1,  1
   900,  422,  294,  127,  70,  17,  10,  1,  1
  2162, 1166,  720,  435, 165,  86,  19, 11,  1, 1
  5417, 2885, 2119, 1110, 608, 208, 104, 21, 12, 1, 1
  ...

Crossrefs

Columns give A003120, A193487, A193488, A193489, A193490. Row sums give A000081.

Sequence in context: A128264 A232435 A114858 * A364271 A352062 A263340

Adjacent sequences: A193488 A193489 A193490 * A193492 A193493 A193494

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jul 27 2011

Status

approved