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Search: id:A007714
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| A007714 |
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Number of 5-level rooted trees with n leaves. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Huberman, B. A. and Hogg, T.; 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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LINKS
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Index entries for sequences related to rooted trees
N. J. A. Sloane, Transforms
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
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FORMULA
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Euler transform applied 4 times to all-1's sequence.
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MAPLE
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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=1..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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MATHEMATICA
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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
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CROSSREFS
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Sequence in context: A147324 A109245 A002221 this_sequence A123011 A006358 A054108
Adjacent sequences: A007711 A007712 A007713 this_sequence A007715 A007716 A007717
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KEYWORD
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easy,nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), Aug 15 1998.
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