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Search: id:A007713
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| A007713 |
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Number of 4-level rooted trees with n leaves. |
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+0
3
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| 1, 4, 10, 30, 75, 206, 518, 1344, 3357, 8429, 20759, 51044, 123973, 299848, 719197, 1716563, 4070800, 9607797, 22555988, 52718749, 122655485, 284207304, 655894527, 1508046031, 3454808143, 7887768997
(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.; 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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P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
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FORMULA
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Euler transform applied thrice 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: b0:= etr(1): b1:= etr(b0): a:= etr(b1): seq (a(n), n=1..26); [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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Adjacent sequences: A007710 A007711 A007712 this_sequence A007714 A007715 A007716
Sequence in context: A047188 A002220 A090578 this_sequence A058488 A036674 A006357
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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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