OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
FORMULA
a(n) ~ c * 2^n * n^(n - 1/3 - log(2/3)/4) / (exp(n) * (log(3/2))^n), where c = 0.253289930600610020471... . - Vaclav Kotesovec, Aug 08 2014
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 21*x^3 + 340*x^4 + 7459*x^5 + 203191*x^6 +...
RELATED SERIES.
A(x)^2 = 1 + 2*x + 5*x^2 + 46*x^3 + 726*x^4 + 15682*x^5 + 423101*x^6 +...
A(x*A(x)^2) = 1 + x + 4*x^2 + 34*x^3 + 540*x^4 + 11696*x^5 + 316071*x^6 +...
A(x*A(x)^2)^2 = 1 + 2*x + 9*x^2 + 76*x^3 + 1164*x^4 + 24744*x^5 + 661010*x^6 +...
A(x)^3 = 1 + 3*x + 9*x^2 + 76*x^3 + 1164*x^4 + 24744*x^5 + 661010*x^6 +...
PROG
(PARI) {a(n)=local(A=[1, 1], Ax); for(i=1, n, A=concat(A, 0); Ax=Ser(A);
A[#A]=Vec(1+subst(Ax^2, x, x*Ax^2) - Ax^3)[#A]); A[n+1]}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 06 2014
STATUS
approved