OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
A(x) = 1 + x*G(2*x)^2, where G(x) = g.f. of A088716, such that a(n) = 2^n*A088716(n)/(n+1) for n>=0.
a(n) = 2^(n-1)*A112916(n-1) for n>0.
G.f. satisfies: A(x) = 1 + x*(d/dx[x*A(x)])^2 = 1 + x*(A(x) + x*A'(x))^2.
a(n) ~ c * n * 2^n * n!, where c = A238223 = 0.21795078944715106549... - Vaclav Kotesovec, Aug 24 2017
PROG
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, (k+1)*(n-k)*a(k)*a(n-k-1)))
(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x*deriv(x*F)^2); return(polcoeff(F, n, x))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 06 2005
STATUS
approved