A000342 Number of n-node rooted trees of height 5. (Formerly M3884 N1594)

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

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.

J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)

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-François Alcover, Feb 07 2016, after Alois P. Heinz in A034781 *)

Crossrefs

Column h=5 of A034781.

Sequence in context: A102841 A036637 A036644 * A189427 A355492 A212339

Adjacent sequences: A000339 A000340 A000341 * A000343 A000344 A000345

Keyword

nonn

Author

N. J. A. Sloane

Status

approved