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A000429 Number of n-node rooted trees of height 8.
(Formerly M4525 N1918)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

REFERENCES

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

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

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

FORMULA

A034825-A034824. (Christian G. Bower).

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 *)

CROSSREFS

Column h=8 of A034781.

Sequence in context: A036633 A036640 A036647 * A055853 A137748 A005024

Adjacent sequences:  A000426 A000427 A000428 * A000430 A000431 A000432

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.