%I M0301 #28 Dec 17 2021 11:11:53

%S 1,1,1,2,2,4,3,7,4,11,6,15,7,24,8,29,12,40,13,51,14,68,19,76,20,107,

%T 23,116,29,147,30,175,31,215,39,229,45,297,46,312,55,387,56,435,57,

%U 513,73,534,74,670,78,705,92,823,93,897,102,1051,117,1082

%N Number of planted trees: all sub-rooted trees from any node are identical; non-root, non-leaf nodes an even distance from the root are of degree 2.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A007439/b007439.txt">Table of n, a(n) for n=1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n+2) = Sum a(k), k|n. Shifts left two places under inverse Moebius transformation.

%F G.f. A(x) satisfies: A(x) = x + x^2 * (1 + A(x) + A(x^2) + A(x^3) + ...). - _Ilya Gutkovskiy_, May 09 2019

%t a[n_] := a[n] = Sum[a[k], {k, Divisors[n-2]}]; a[1] = a[2] = 1; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, May 15 2013 *)

%o (Haskell)

%o a007439 n = a007439_list !! (n-1)

%o a007439_list = 1 : 1 : f 2 where

%o f x = (sum $ map a007439 $ a027750_row (x - 1)) : f (x + 1)

%o -- _Reinhard Zumkeller_, Dec 20 2014

%Y Cf. A003238, A007562.

%Y Cf. A027750.

%K nonn,nice,eigen,look

%O 1,4

%A _N. J. A. Sloane_

%E New description from _Christian G. Bower_, Oct 15 1998