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 A007714 Number of 5-level rooted trees with n leaves. 6
 1, 1, 5, 15, 55, 170, 571, 1789, 5727, 17836, 55627, 171169, 524879, 1595896, 4829894, 14527981, 43497312, 129588391, 384430264, 1135607519, 3341662498, 9796626673, 28620419254, 83334382425, 241879403752, 699937499318, 2019607806247, 5811320364410, 16677611788799 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5. 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. N. J. A. Sloane, Transforms FORMULA Euler transform applied 4 times to all-1's sequence. MAPLE with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: b[0]:= etr(1): for k from 1 to 2 do b[k]:= etr(b[k-1]) od: a:= etr(b[2]): seq(a(n), n=0..25); # Alois P. Heinz, Sep 08 2008 MATHEMATICA i[ n_, m_ ] := 1 /; m==1 || n==0; i[ n_, m_ ] := (i[ n, m ]=1/n Sum[ i[ k, m ] Plus @@ ((# i[ #, m-1 ])& /@ Divisors[ n-k ]), {k, 0, n-1} ]) /; n>0 && m>1 (* Second program: *) A[0|1, _] = A[_, 1] = 1; A[n_, k_] := A[n, k] = Sum[DivisorSum[j, A[#, k-1] * #&]*A[n-j, k], {j, 1, n}]/n; a[n_] := A[n, 5]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 16 2018, after A290353 *) CROSSREFS Column k=5 of A290353. Sequence in context: A109245 A243076 A002221 * A123011 A006358 A054108 Adjacent sequences:  A007711 A007712 A007713 * A007715 A007716 A007717 KEYWORD easy,nonn AUTHOR EXTENSIONS More terms from Christian G. Bower, Aug 15 1998 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)