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A290359 The tenth Euler transform of the sequence with g.f. 1+x. 2
1, 1, 10, 55, 385, 2365, 15367, 96613, 611644, 3832477, 23970089, 149170604, 925530638, 5722654098, 35282873191, 216928671076, 1330360845060, 8139139896353, 49683631194244, 302640125458942, 1839793530751731, 11163107720200726, 67610680329079976 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Also the number of 10-level rooted trees with n leaves. All n leaves are in level 10.
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)^A290358(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, 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 *)
CROSSREFS
Column k=10 of A290353.
Cf. A290358.
Sequence in context: A188168 A199413 A054629 * A030114 A001557 A367938
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 28 2017
STATUS
approved

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Last modified April 15 13:47 EDT 2024. Contains 371689 sequences. (Running on oeis4.)