0,3

Approaches 1.5028368...^(2^n). Row sum of A065329 as square array. - Henry Bottomley (se16(AT)btinternet.com), Oct 29 2001. Also row sum of square array A073345 (AK).

I. M. H. Etherington, On non-associative combinations, Proc. Royal Soc. Edinburgh, 59 (Part 2, 1938-39), 153-162.

T. K. Moon, Enumerations of binary trees, types of trees and the number of reversiblevariable length codes, submitted to Discrete Applied Mathematics, 2000.

David Wasserman, Table of n, a(n) for n = 0..13

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

H. Bottomley, Illustration of initial terms

C. Lenormand, Arbres et permutations II, see p. 6

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for "core" sequences

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Index entries for sequences related to parenthesizing

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

a(n+1) = 2*a(n)*(a(0)+...+a(n-1))+a(n)^2.

a(n+1) = a(n)^2+a(n)+a(n)*sqrt(4*a(n)-3), if n>0.

a(n+1) = A003095(n+1)-A003095(n) = A003095(n)^2- A003095(n)+1. - Henry Bottomley (se16(AT)btinternet.com), Apr 26 2001

a(n)=A059826(A003095(n-1))

s := proc(n) local i, j, ans; ans := [ 1 ]; for i to n do ans := [ op(ans), 2*(add(j, j=ans)-ans[ i ])*ans[ i ]+ans[ i ]^2 ] od; RETURN(ans); end; s(10);

(PARI) a(n)=if(n<=1, n >= 0, a(n-1)*(a(n-1)+a(n-2)+a(n-1)/a(n-2))); b(n)=if(n<1, 0, 1+b(n-1)^2); A003095(n)=b(n); A059826(n)=(n^2-n+1)*(n^2+n+1); A002061(n)=n^2-n+1

Cf. A002658, A056207, A002449, A003095.

Cf. A004019.

Adjacent sequences: A001696 A001697 A001698 this_sequence A001700 A001701 A001702

Sequence in context: A093549 A012044 A098918 this_sequence A057600 A079269 A127104

nonn,easy,core,nice

njas, Jeffrey Shallit