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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). 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..35.

H. Bottomley, Illustration of initial terms

FORMULA

T(n,k) = Sum_j{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: A078341 A199459 A316649 * A108998 A309993 A248673

Adjacent sequences:  A065326 A065327 A065328 * A065330 A065331 A065332

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Oct 29 2001

STATUS

approved

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Last modified August 8 04:32 EDT 2020. Contains 336290 sequences. (Running on oeis4.)