A271205 Number T(m,n) of series-reduced free trees with n nodes of which exactly m >= 3 are leaves, m+1 <= n <= 2m-2.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 4, 4, 2, 1, 3, 6, 10, 8, 4, 1, 3, 9, 17, 22, 15, 6, 1, 4, 12, 30, 47, 53, 32, 11, 1, 4, 16, 44, 91, 127, 121, 66, 18, 1, 5, 20, 67, 158, 282, 346, 292, 142, 37, 1, 5, 25, 91, 258, 539, 841, 921, 688, 306, 66, 1, 6, 30, 126, 397, 978, 1804, 2498, 2456, 1662, 672, 135, 1, 6, 36, 163, 588, 1636, 3550, 5856, 7260, 6489, 3978, 1483, 265, 1, 7, 42, 213, 838, 2638, 6495, 12554, 18636, 20946, 17082, 9629, 3316, 552, 1, 8

Offset: 3

Author

Stephan Beyer, Apr 01 2016

Keywords

• nonn
• tabf

Comments

The sequence of row sums a(m) = Sum_{n} T(m,n) is A007827.

The sequence of column sums a(n) = Sum_{m} T(m,n) is A000014.

Examples

			m\n | 3 4 5 6 7 8 9 10 11 12 13 14 15 16  17  18 19 20
-------------------------------------------------------
3   | . 1 . . . . .  .  .  .  .  .  .  .   .   .  .  .
4   | . . 1 1 . . .  .  .  .  .  .  .  .   .   .  .  .
5   | . . . 1 1 1 .  .  .  .  .  .  .  .   .   .  .  .
6   | . . . . 1 2 2  2  .  .  .  .  .  .   .   .  .  .
7   | . . . . . 1 2  4  4  2  .  .  .  .   .   .  .  .
8   | . . . . . . 1  3  6 10  8  4  .  .   .   .  .  .
9   | . . . . . . .  1  3  9 17 22 15  6   .   .  .  .
10  | . . . . . . .  .  1  4 12 30 47 53  32  11  .  .
11  | . . . . . . .  .  .  1  4 16 44 91 127 121 66 18
		

Links

• Stephan Beyer, Python code to generate the sequence on GitHub Gist

Crossrefs

Cf. A000014, A007827.

Transpose of A271362.