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A290356
The seventh Euler transform of the sequence with g.f. 1+x.
3
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
0,3
COMMENTS
Also the number of 7-level rooted trees with n leaves. All n leaves are in level 7.
LINKS
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.
FORMULA
G.f.: Product_{j>0} 1/(1-x^j)^A290355(j).
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 *)
CROSSREFS
Column k=7 of A290353.
Cf. A290355.
Sequence in context: A354456 A249872 A238448 * A025030 A001554 A370243
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 28 2017
STATUS
approved