A065329 Square array read by antidiagonals giving number of binary trees of height n with k points on the n-th level (n,k>0).

1, 0, 2, 0, 1, 8, 0, 0, 8, 80, 0, 0, 4, 144, 4160, 0, 0, 1, 168, 13888, 5632640, 0, 0, 0, 138, 31776, 36109952, 5163215782400, 0, 0, 0, 80, 54792, 158572864, 64827181969920, 2169236189050838782284800, 0, 0, 0, 32, 74624, 531441232, 552146121580800

Offset: 1

Author

Henry Bottomley, Oct 29 2001

Keywords

• nonn
• tabl

Examples

			Square array starts:
   1,   0,   0,   0,   0,   0,   0,   0,   0,   0, ...
   2,   1,   0,   0,   0,   0,   0,   0,   0,   0, ...
   8,   8,   4,   1,   0,   0,   0,   0,   0,   0, ...
  80, 144, 168, 138,  80,  32,   8,   1,   0,   0, ...
  ...
		

Links

• H. Bottomley, Illustration of initial terms

Crossrefs

Row sums are A001699.

Cf. A073345, A073429.

Formula

T(n,k) = Sum_{2j >= k} (C(2j,k)*T(n-1,j)) starting with T(1,1) = 1 and T(1,k) = 0 if k>1.

Extensions

More terms from Sean A. Irvine, Aug 30 2023