A290359 The tenth Euler transform of the sequence with g.f. 1+x.

1, 1, 10, 55, 385, 2365, 15367, 96613, 611644, 3832477, 23970089, 149170604, 925530638, 5722654098, 35282873191, 216928671076, 1330360845060, 8139139896353, 49683631194244, 302640125458942, 1839793530751731, 11163107720200726, 67610680329079976

Offset: 0

Author

Alois P. Heinz, Jul 28 2017

Keywords

• nonn

Comments

Also the number of 10-level rooted trees with n leaves. All n leaves are in level 10.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
• Index entries for sequences related to rooted trees

Crossrefs

Column k=10 of A290353.

Cf. A290358.

Programs

Maple

with(numtheory):
b:= proc(n, k) option remember; `if`(n<2, 1, `if`(k=0, 0, add(
      add(b(d, k-1)*d, d=divisors(j))*b(n-j, k), j=1..n)/n))
    end:
a:= n-> b(n, 10):
seq(a(n), n=0..30);

Mathematica

b[n_, k_]:=b[n, k]=If[n<2, 1, If[k==0, 0, Sum[Sum[b[d, k - 1]*d, {d, Divisors[j]}] b[n - j, k], {j, n}]/n]]; Table[b[n, 10], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017 *)

Formula

G.f.: Product_{j>0} 1/(1-x^j)^A290358(j).