OFFSET
1,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 4.1920029654932692520828... and c = 0.1046247209912855075794... . - Vaclav Kotesovec, May 03 2016
EXAMPLE
G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 + 474*x^8 + 1650*x^9 + 5865*x^10 + 21194*x^11 + 77623*x^12 +...
where A( x - A(x^4)/x^2 ) = x.
RELATED SERIES.
Let B(x) be the series reversion of the g.f. A(x) so that A(B(x)) = x, then
B(x) = x - x^2 - x^6 - 2*x^10 - 5*x^14 - 14*x^18 - 43*x^22 - 140*x^26 - 474*x^30 - 1650*x^34 - 5865*x^38 - 21194*x^42 - 77623*x^46 +...
such that B(x) = x - A(x^4)/x^2.
PROG
(PARI) {a(n) = my(A=x); for(i=1, n, A = serreverse( x - subst(A, x, x^4 +x^3*O(x^n))/x^2 )); polcoeff(A, n)}
for(n=1, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 29 2016
STATUS
approved