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 A290358 The ninth Euler transform of the sequence with g.f. 1+x. 3
 1, 1, 9, 45, 285, 1575, 9237, 52221, 297633, 1676364, 9425128, 52688379, 293582296, 1629482947, 9015732880, 49727160669, 273504111761, 1500271605182, 8209029290412, 44811239964075, 244069307558722, 1326536980923855, 7195340066129605, 38953817605037254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of 9-level rooted trees with n leaves. All n leaves are in level 9. 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. FORMULA G.f.: Product_{j>0} 1/(1-x^j)^A290357(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, 9): 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, 9], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017, after Maple code *) CROSSREFS Column k=9 of A290353. Cf. A290357. Sequence in context: A054628 A132133 A009410 * A030113 A001556 A230063 Adjacent sequences:  A290355 A290356 A290357 * A290359 A290360 A290361 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 28 2017 STATUS approved

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Last modified May 24 01:29 EDT 2019. Contains 323528 sequences. (Running on oeis4.)