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A000342 Number of n-node rooted trees of height 5.
(Formerly M3884 N1594)
2
0, 0, 0, 0, 0, 1, 5, 19, 61, 180, 498, 1323, 3405, 8557, 21103, 51248, 122898, 291579, 685562, 1599209, 3705122, 8532309, 19543867, 44552066, 101124867, 228640542, 515125815, 1156829459, 2590247002, 5784031485, 12883390590, 28629914457 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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

FORMULA

A001385-A001384. (Christian G. Bower).

MAPLE

For Maple program see link in A000235.

MATHEMATICA

f[n_] := Nest[CoefficientList[Series[Product[1/(1 - x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x] &, {1}, n]; f[5]-f[4] (* Geoffrey Critzer, Aug 01 2013 )

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, 5] - b[n-1, n-1, 4]; Array[a, 40] (* Jean-Fran├žois Alcover, Feb 07 2016, after Alois P. Heinz in A034781 *)

CROSSREFS

Column h=5 of A034781.

Sequence in context: A102841 A036637 A036644 * A189427 A212339 A072111

Adjacent sequences:  A000339 A000340 A000341 * A000343 A000344 A000345

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 26 04:27 EDT 2017. Contains 292502 sequences.