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Search: id:A001384
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| A001384 |
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Number of n-node trees of height at most 4.
(Formerly M1172 N0449)
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+0
4
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| 1, 1, 1, 2, 4, 9, 19, 42, 89, 191, 402, 847, 1763, 3667, 7564, 15564, 31851, 64987, 132031, 267471, 539949, 1087004, 2181796, 4367927, 8721533, 17372967, 34524291, 68456755, 135446896, 267444085, 527027186, 1036591718, 2035083599
(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
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 63
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 A001383 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: A000041:= etr (n->1): b1:= etr (k-> A000041(k-1)): A001383:= n->`if`(n=0, 1, b1(n-1)): b2:= etr (A001383): a:= n->`if`(n=0, 1, b2(n-1)): seq (a(n), n=0..32); [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: A141683 A078039 A036622 this_sequence A089941 A127681 A112569
Adjacent sequences: A001381 A001382 A001383 this_sequence A001385 A001386 A001387
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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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