A000429 Number of n-node rooted trees of height 8.

0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 43, 188, 728, 2593, 8706, 27961, 86802, 262348, 776126, 2256418, 6466614, 18311915, 51334232, 142673720, 393611872, 1078955836, 2941029334, 7977065816, 21541492856, 57942770689, 155304829763, 414934057486

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• N. J. A. Sloane, Table of n, a(n) for n=1..200
• J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

Column h=8 of A034781.

Programs

Maple

For Maple program see link in A000235.

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1 || k < 1, 0, Sum[ Binomial[b[i - 1, i - 1, k - 1] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 8] - b[n - 1, n - 1, 7]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *)

Formula

a(n) = A034825(n) - A034824(n). - Christian G. Bower