OFFSET
1,4
COMMENTS
Given g.f. A(x), A(A(x)) equals the g.f. of A213010.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..256
FORMULA
a(n) == 1 (mod 4).
EXAMPLE
G.f.: A(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 +...
where
A(A(x)) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...
A(A(A(A(x)))) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...
PROG
(PARI) {a(n)=local(A=x+x^2, B=x+2*x^2); for(i=1, n, B=x+x^2+x*subst(B, x, B+x*O(x^n)));
for(i=1, n, A=(A+subst(B, x, serreverse(A+x*O(x^n))))/2); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 01 2012
STATUS
approved