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Search: id:A001385
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| A001385 |
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Number of n-node trees of height at most 5.
(Formerly M1177 N0453)
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+0
5
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| 1, 1, 1, 2, 4, 9, 20, 47, 108, 252, 582, 1345, 3086, 7072, 16121, 36667, 83099, 187885, 423610, 953033, 2139158, 4792126, 10714105, 23911794, 53273599, 118497834, 263164833, 583582570, 1292276355, 2857691087, 6311058671, 13919982308
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n=0..200
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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Take Euler transform of A001384 and shift right. (Christian G. Bower (bowerc(AT)usa.net)).
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MAPLE
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For Maple program see link in A000235.
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: shr:= proc(p) n->`if`(n=0, 1, p(n-1)) end: b[0]:= etr(n->1): for j from 1 to 3 do b[j]:= etr (shr(b[j-1])) od: a:= shr(b[3]): seq (a(n), n=0..31); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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CROSSREFS
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See A001383 for details.
Sequence in context: A110198 A104508 A036623 this_sequence A039808 A138164 A130802
Adjacent sequences: A001382 A001383 A001384 this_sequence A001386 A001387 A001388
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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