A215119 G.f. A(x) satisfies: A(A(A(A(A(x))))) = G(x) where G(x) = x + 4*x^2 + x*G(G(G(G(G(x))))) is the g.f. of A215118.

1, 1, 1, 101, 2301, 82601, 3287001, 149411501, 7474902101, 406765054801, 23836604715601, 1493376284080501, 99459838574595501, 7009748111184956601, 520845172037612209801, 40672220108202107951101, 3328819620490715884626501, 284871268231239093741932001

Offset: 1

Author

Paul D. Hanna, Aug 03 2012

Keywords

• nonn

Comments

a(n) == 1 (mod 100).

Examples

			G.f.: A(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 +...
Let G(x) = A(A(A(A(A(x))))):
G(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 + 25390625*x^7 +...
such that G(x) = x + 4*x^2 + x*G(G(G(G(G(x))))):
G(G(G(G(G(x))))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 + 25390625*x^6 +...
		

Crossrefs

Cf. A215118, A213009, A215115, A215117.

Programs

PARI

{a(n)=local(A=x+x^2,B=x+4*x^2);for(i=1,n+1,B=x+4*x^2+x*subst(B,x,subst(B,x,subst(B,x,subst(B,x,B+x^2*O(x^n))))));
for(j=1, n+1, A=round((4*A+subst(B, x, serreverse(subst(A,x,subst(A,x,subst(A,x,A+x^2*O(x^n)))))))/5));; polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))