OFFSET
1,2
COMMENTS
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..200
FORMULA
G.f. A(x) satisfies: A( x*G(x^2) - 5*x^2 ) = x, where G(x)^2 = G(x^2) + 20*x, and G(x) is the g.f. of A264414.
EXAMPLE
G..f.: A(x) = x + 5*x^2 + 40*x^3 + 375*x^4 + 3845*x^5 + 41825*x^6 + 474450*x^7 + 5552250*x^8 + 66548785*x^9 + 812875800*x^10 + 10082125950*x^11 + 126637168125*x^12 +...
where A(x)^2 = A( x^2 + 10*x*A(x)^2 ).
RELATED SERIES.
A(x)^2 = x^2 + 10*x^3 + 105*x^4 + 1150*x^5 + 13040*x^6 + 152100*x^7 + 1815375*x^8 + 22078750*x^9 + 272728845*x^10 + 3412891200*x^11 + 43178951325*x^12 +...
Let B(x) be the series reversion of the g.f. A(x), A(B(x)) = x, then:
B(x) = x - 5*x^2 + 10*x^3 - 45*x^5 + 450*x^7 - 5535*x^9 + 75600*x^11 - 1106100*x^13 + 16953750*x^15 +...+ A264414(n)*x^(2*n+1) +...
such that B(x) = x*G(x^2) - 5*x^2 where G(x)^2 = G(x^2) + 20*x, and G(x) is the g.f. of A264414.
PROG
(PARI) {a(n) = my(A=x+x^2, X=x+x*O(x^n)); for(i=1, n, A = subst(A, x, x^2 + 10*X*A^2)^(1/2) ); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 17 2016
STATUS
approved