OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..81
FORMULA
a(n) = 2^(n-1)*Sum_{k=0..n-1} a(k)*a(n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Feb 09 2010
a(n) ~ c * 2^(n*(n+1)/2), where c = 0.715337433614869740944075474484711589980951273610257702786245519231799678... - Vaclav Kotesovec, Nov 04 2021
MATHEMATICA
nmax = 15; A[_] = 0; Do[A[x_] = 1 + x*A[2*x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 04 2021 *)
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^2); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, 2^(n-1)*sum(k=0, n-1, a(k)*a(n-k-1))) \\ Paul D. Hanna, Feb 09 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 02 2007
STATUS
approved