OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..330 (terms 1..200 from Paul D. Hanna)
FORMULA
a(n) ~ (-1)^n * c * 6^n * n! / (n^(1/3) * (log(3))^n), where c = 0.04217549814791850977595... - Vaclav Kotesovec, Oct 09 2017
EXAMPLE
G.f.: A(x) = x + 2*x^2 - 12*x^3 + 216*x^4 - 5616*x^5 + 186624*x^6 - 7387200*x^7 + 335736576*x^8 - 17124804864*x^9 + 965515500288*x^10 - 59526188983296*x^11 + 3980690988235776*x^12 - 286917239797788672*x^13 + 22174720816561975296*x^14 - 1829668999418480590848*x^15 +...
such that A( 4*x - 3*A(x) ) = x - 4*x^2.
RELATED SERIES.
Define Ai(x) such that Ai(A(x)) = x, then Ai(x) begins:
Ai(x) = x - 2*x^2 + 20*x^3 - 376*x^4 + 9872*x^5 - 325056*x^6 + 12684480*x^7 - 567616512*x^8 + 28519993088*x^9 - 1585862993152*x^10 + 96566543541248*x^11 +...
where Ai(x - 4*x^2) = 4*x - 3*A(x).
PROG
(PARI) {a(n) = my(A=x, V=[1, 2]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(A, x, 4*x - 3*A) )[#V]/2 ); V[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 23 2017
STATUS
approved