A215118 G.f. satisfies: A(x) = x + 4*x^2 + x*A(A(A(A(A(x))))).

1, 5, 25, 625, 18125, 628125, 25390625, 1158515625, 58308203125, 3190470703125, 187941103515625, 11832996337890625, 791834056298828125, 56063448811767578125, 4184231129351806640625, 328154000925299072265625, 26970505516268341064453125, 2317475342690856231689453125

Offset: 1

Author

Paul D. Hanna, Aug 03 2012

Keywords

• nonn

Comments

The (1/5)-iteration of the g.f. equals an integer series (A215119).

Examples

			G.f.: A(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 + ...
where
A(A(A(A(x)))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 + ...
Related expansions.
Let E(E(E(E(E(x))))) = A(x), then E(x) is an integer series where:
E(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 + ...
where the coefficients of E(x) are congruent to 1 modulo 100.
		

Crossrefs

Cf. A215119, A213010, A215114, A215116.

Programs

PARI

{a(n) = my(A=x+4*x^2); for(i=1,n,A=x+4*x^2+x*subst(A,x,subst(A,x,subst(A,x,subst(A,x,A+x*O(x^n)))))); polcoef(A, n)}
for(n=1, 31, print1(a(n), ", "))