A363273 Irregular triangle read by rows: T(n,k) = number of unlabeled binary rooted trees with n leaves, where both children have at least k leaves, 1 <= k <= n/2.

1, 1, 2, 1, 3, 1, 6, 3, 1, 11, 5, 2, 23, 12, 6, 3, 46, 23, 12, 6, 98, 52, 29, 18, 6, 207, 109, 63, 40, 18, 451, 244, 146, 100, 54, 21, 983, 532, 325, 227, 135, 66, 2179, 1196, 745, 538, 342, 204, 66, 4850, 2671, 1688, 1237, 823, 529, 253, 10905, 6055, 3876, 2893, 1991, 1370, 782, 276

Offset: 2

Author

Harry Richman, May 24 2023

Keywords

• nonn
• tabf

Examples

			Table begins:
  1;
  1;
  2,   1;
  3,   1;
  6,   3,  1;
 11,   5,  2;
 23,  12,  6,  3;
 46,  23, 12,  6;
 98,  52, 29, 18,  6;
207, 109, 63, 40, 18;
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..2501 (rows 1..100)

Crossrefs

First column k = 1 is A001190.

Sums along upwards diagonals are A000671.

Cf. A363272.

Programs

PARI

T(n)={my(A=vector(n), R=vector(n)); A[1]=1; R[1]=[]; for(i=2, n, my(t=vector(i\2, j, if(2*jAndrew Howroyd, Jan 01 2024

Formula

T(n,k) = Sum_{j >= k} A363272(n,j).

Sum_{k >= 1} T(n-k, k) = A000671(n-2).

Extensions

Terms a(27) and beyond from Andrew Howroyd, Jan 01 2024