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A290358
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The ninth Euler transform of the sequence with g.f. 1+x.
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3
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1, 1, 9, 45, 285, 1575, 9237, 52221, 297633, 1676364, 9425128, 52688379, 293582296, 1629482947, 9015732880, 49727160669, 273504111761, 1500271605182, 8209029290412, 44811239964075, 244069307558722, 1326536980923855, 7195340066129605, 38953817605037254
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OFFSET
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0,3
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COMMENTS
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Also the number of 9-level rooted trees with n leaves. All n leaves are in level 9.
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LINKS
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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.
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FORMULA
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G.f.: Product_{j>0} 1/(1-x^j)^A290357(j).
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MAPLE
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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, 9):
seq(a(n), n=0..30);
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MATHEMATICA
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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, 9], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017, after Maple code *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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