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 A001385 Number of n-node trees of height at most 5. (Formerly M1177 N0453) 5
 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, 30664998056, 67473574130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n+1) is also the number of n-vertex graphs that do not contain a P_4, C_4, or K_6 as induced subgraph (K_6-free trivially perfect graphs, cf. A123467). - Falk Hüffner, Jan 10 2016 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS N. J. A. Sloane, Table of n, a(n) for n=0..200 J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478. N. J. A. Sloane, Transforms FORMULA Take Euler transform of A001384 and shift right. (Christian G. Bower). MAPLE 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..35); # Alois P. Heinz, Sep 08 2008 MATHEMATICA Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x]&, {1}, 5], 1] (* Geoffrey Critzer, Aug 01 2013 *) CROSSREFS See A001383 for details. Sequence in context: A110198 A104508 A036623 * A039808 A138164 A130802 Adjacent sequences:  A001382 A001383 A001384 * A001386 A001387 A001388 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)