0,4

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

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).

N. J. A. Sloane, Table of n, a(n) for n=0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 62

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

G.f.: S[ 3 ] := x*Product (1 - x^k)^(-p(k-1)), where p(k) = number of partitions of k.

a(n+1) is the Euler transform of p(n-1), where p() = A000041 is the partition function. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 01 2006

s[ 2 ] := x/product('1-x^i', 'i'=1..30); # G.f. for trees of ht <=2, A000041

for k from 3 to 12 do # gets g.f. for trees of ht <= 3, 4, 5, ...

s[ k ] := series(x/product('(1-x^i)^coeff(s[ k-1 ], x, i)', 'i'=1..30), x, 31); od:

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): a:= n->`if`(n=0, 1, etr (k-> A000041(k-1))(n-1)): seq (a(n), n=0..36); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]

Cf. A000041, A001383-A001385, A034823-A034826.

Sequence in context: A118870 A088532 A036621 this_sequence A108564 A066369 A000078

Adjacent sequences: A001380 A001381 A001382 this_sequence A001384 A001385 A001386

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).