OFFSET
0,3
LINKS
Vaclav Kotesovec,Table of n, a(n) for n = 0..80
FORMULA
a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 2^i * a(i) * a(j) * a(n-i-j-1). -Ilya Gutkovskiy,Nov 12 2021
a(n) ~ c * 2^(n*(n-1)/2), where c = 8.922794036651587033803872123786584213844... -Vaclav Kotesovec,Nov 13 2021
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 348*x^4 + 7078*x^5 +...
A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 770*x^4 + 15084*x^5 +...
MATHEMATICA
nmax = 20; A[_] = 0; Do[A[x_] = 1 + x*A[x]^2*A[2*x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (*Vaclav Kotesovec,Nov 13 2021 *)
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*A^2*subst(A, x, 2*x) ); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna,Dec 05 2009
STATUS
approved