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A007439 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.

%I A007439 M0301 #28 Dec 17 2021 11:11:53
%S A007439 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 A007439 23,116,29,147,30,175,31,215,39,229,45,297,46,312,55,387,56,435,57,
%U A007439 513,73,534,74,670,78,705,92,823,93,897,102,1051,117,1082
%N A007439 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 A007439 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007439 T. D. Noe, <a href="/A007439/b007439.txt">Table of n, a(n) for n=1..1000</a>
%H A007439 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A007439 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A007439 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A007439 a(n+2) = Sum a(k), k|n. Shifts left two places under inverse Moebius transformation.
%F A007439 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 A007439 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 A007439 (Haskell)
%o A007439 a007439 n = a007439_list !! (n-1)
%o A007439 a007439_list = 1 : 1 : f 2 where
%o A007439    f x = (sum $ map a007439 $ a027750_row (x - 1)) : f (x + 1)
%o A007439 -- _Reinhard Zumkeller_, Dec 20 2014
%Y A007439 Cf. A003238, A007562.
%Y A007439 Cf. A027750.
%K A007439 nonn,nice,eigen,look
%O A007439 1,4
%A A007439 _N. J. A. Sloane_
%E A007439 New description from _Christian G. Bower_, Oct 15 1998