A034825 -id:A034825 - cp's OEIS frontend

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

N. J. A. Sloane

nonn

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).

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

Column h=8 of A034781.

Maple
```
For Maple program see link in A000235.
```

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 *)

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

A034826 Number of n-node rooted trees of height at most 9.

Original entry on oeis.org

1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1841, 4755, 12410, 32558, 85849, 226980, 601373, 1594870, 4232100, 11230771, 29798539, 79034638, 209526631, 555172356, 1470195001, 3891131705, 10292857772, 27212082536, 71905725130, 189911518888

Offset: 0

N. J. A. Sloane

nonn

N. J. A. Sloane, Table of n, a(n) for n=0..200
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees

See A001383 for details.

For Maple program see link in A000235.
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: shr:= proc(p) n->`if`(n=0, 1,p(n-1)) end: b[0]:= etr(n->1): for j from 1 to 7 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[7]): seq(a(n), n=0..40); # Alois P. Heinz, Sep 08 2008

etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; b]; shr[p_] = If[# == 0, 1, p[#-1]]&; b[0] = etr[1&]; For[j = 1, j <= 7, j++, b[j] = etr[shr[b[j-1]]]]; a = shr[b[7]]; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)

Take Euler transform of A034825 and shift right. (Christian G. Bower).

cp's OEIS Frontend

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

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