A213009 G.f. A(x) satisfies: A(A(x)) = x+x^2 + x*A(A(A(A(x)))).

1, 1, 1, 5, 21, 125, 825, 6133, 49925, 439417, 4142945, 41544161, 440710117, 4924691541, 57766255689, 709205703565, 9090541134373, 121389729560633, 1685431945085489, 24289856880005441, 362776874949660485, 5606980244843123077, 89560387072919814553

Offset: 1

Author

Paul D. Hanna, Jun 01 2012

Keywords

• nonn

Comments

Given g.f. A(x), A(A(x)) equals the g.f. of A213010.

Examples

			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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..256

Crossrefs

Cf. A213010, A215115, A215117, A215119.

Programs

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),", "))

Formula

a(n) == 1 (mod 4).