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

1,3

Links

Table of n, a(n) for n=1..43.

H. Bottomley, Illustration of initial terms

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.

Example

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, ...
  ...

Crossrefs

Row sums are A001699.

Cf. A073345, A073429.

Sequence in context: A371762 A199459 A316649 * A352772 A108998 A356265

Adjacent sequences: A065326 A065327 A065328 * A065330 A065331 A065332

Keyword

nonn,tabl

Author

Henry Bottomley, Oct 29 2001

Extensions

More terms from Sean A. Irvine, Aug 30 2023

Status

approved