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 A290357 The eighth Euler transform of the sequence with g.f. 1+x. 3
 1, 1, 8, 36, 204, 1002, 5244, 26328, 133476, 667335, 3331117, 16516607, 81607176, 401407499, 1967534543, 9609826869, 46788348316, 227114265649, 1099339308308, 5307155062783, 25556511343601, 122773840789344, 588473630650319, 2814565652799711, 13433897987956859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of 8-level rooted trees with n leaves. All n leaves are in level 8. 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)^A290356(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, 8): 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, 8], {n, 0, 30}] (* Indranil Ghosh, Jul 30 2017, after Maple code *) CROSSREFS Column k=8 of A290353. Cf. A290356. Sequence in context: A019022 A079819 A238815 * A030112 A001555 A032770 Adjacent sequences:  A290354 A290355 A290356 * A290358 A290359 A290360 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 28 2017 STATUS approved

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Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)