Voozh

A063573

First differences of A002065.

1, 2, 10, 170, 33490, 1133870930, 1285739648704587610, 1653126447166808568966775665261637370, 2732827050322355127169206170438813670862431231469970351394153223391753890

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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 86B, Proceedings of the 34th Conf. on Formal Power Series and Algebraic Combinatorics (Bangalore, India, 2022). See also.

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