A290356 The seventh Euler transform of the sequence with g.f. 1+x.

1, 1, 7, 28, 140, 602, 2772, 12166, 54046, 236093, 1030101, 4458247, 19223202, 82448782, 352247250, 1498724840, 6353940527, 26844401919, 113051495750, 474652297902, 1987159118837, 8296760311018, 34551340915438, 143533939056129, 594877730354756

Offset: 0

Author

Alois P. Heinz, Jul 28 2017

Keywords

• nonn

Comments

Also the number of 7-level rooted trees with n leaves. All n leaves are in level 7.

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=7 of A290353.

Cf. A290355.

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, 7):
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, 7], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017, after Maple code *)

Formula

G.f.: Product_{j>0} 1/(1-x^j)^A290355(j).