OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
FORMULA
a(n) ~ c * 2^n * n! / n^(5/2), where c = 4.72771780666962546492... - Vaclav Kotesovec, Nov 21 2017
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 21*x^3 + 132*x^4 + 960*x^5 + 7944*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 60*x^2 + 448*x^3 + 3422*x^4 + 27168*x^5 + 226960*x^6 +...
d/dx x*A(x)^8 = 1 + 16*x + 180*x^2 + 1792*x^3 + 17110*x^4 + 163008*x^5 +...
(d/dx x*A(x)^8)^(1/4) = 1 + 4*x + 21*x^2 + 132*x^3 + 960*x^4 + 7944*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(x*A^8+x*O(x^n))^(1/4)); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 24 2013
STATUS
approved