%I #18 Apr 22 2022 18:11:39
%S 1,2,10,170,33490,1133870930,1285739648704587610,
%T 1653126447166808568966775665261637370
%N First differences of A002065.
%C Number of trees of height n generated by unary and binary composition. - Claude Lenormand (claude.lenormand(AT)free.fr), Sep 05 2001
%H Michael De Vlieger, <a href="/A063573/b063573.txt">Table of n, a(n) for n = 0..11</a>
%H Samuele Giraudo, <a href="https://arxiv.org/abs/2204.03586">The combinator M and the Mockingbird lattice</a>, arXiv:2204.03586 [math.CO], 2022.
%H Samuele Giraudo, <a href="https://igm.univ-mlv.fr/~giraudo/Data/Papers/Mockingbird%20lattices.pdf">Mockingbird lattices</a>, Séminaire Lotharingien de Combinatoire XX, Proceedings of the 34th Conf. on Formal Power, Series and Algebraic Combinatorics (Bangalore, India, 2022).
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F a(n) = a(n-1)^2 + 2 a(n-1) sqrt(a(n-1)-1) + a(n-1) for n > 0. [_Charles R Greathouse IV_, Dec 29 2011]
%t a[0] = 1; Do[a[n] = a[n - 1]^2 + 2 a[n - 1] Sqrt[a[n - 1] - 1] + a[n - 1], {n, 7}]; Array[a, 8, 0] (* _Michael De Vlieger_, Apr 13 2022 *)
%o (PARI) a(n)=if(n,my(k=a(n-1));k^2+2*k*sqrtint(k-1)+k,1) \\ _Charles R Greathouse IV_, Dec 29 2011
%Y Cf. A002065.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Sep 06 2001