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A000418 Number of n-node rooted trees of height 7.
(Formerly M4408 N1862)
2
0, 0, 0, 0, 0, 0, 0, 1, 7, 34, 136, 487, 1615, 5079, 15349, 45009, 128899, 362266, 1002681, 2740448, 7411408, 19865445, 52840977, 139624510, 366803313, 958696860, 2494322662, 6463281890, 16686206047, 42935345688, 110142163940, 281763465941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

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

A034824-A034823. (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, 7] - b[n - 1, n - 1, 6]; Array[a, 40] (* Jean-Fran├žois Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *)

CROSSREFS

Column h=7 of A034781.

Sequence in context: A036632 A036639 A036646 * A055852 A122611 A219756

Adjacent sequences:  A000415 A000416 A000417 * A000419 A000420 A000421

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 23 21:31 EDT 2017. Contains 283985 sequences.