A063573 First differences of A002065.

1, 2, 10, 170, 33490, 1133870930, 1285739648704587610, 1653126447166808568966775665261637370

Offset

0,2

Comments

Number of trees of height n generated by unary and binary composition. - Claude Lenormand (claude.lenormand(AT)free.fr), Sep 05 2001

Links

Michael De Vlieger, Table of n, a(n) for n = 0..11

Samuele Giraudo, The combinator M and the Mockingbird lattice, arXiv:2204.03586 [math.CO], 2022.

Samuele Giraudo, Mockingbird lattices, Séminaire Lotharingien de Combinatoire XX, Proceedings of the 34th Conf. on Formal Power, Series and Algebraic Combinatorics (Bangalore, India, 2022).

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Formula

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]

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A002065.

Sequence in context: A260122 A132341 A069994 * A368573 A356887 A086675

Adjacent sequences: A063570 A063571 A063572 * A063574 A063575 A063576

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2001

Status

approved