A215117 G.f. A(x) satisfies: A(A(A(A(x)))) = G(x) where G(x) = x + 3*x^2 + x*G(G(G(G(x)))) is the g.f. of A215116.

1, 1, 1, 49, 721, 17281, 452065, 13511953, 443435185, 15816390241, 606861668161, 24867738772849, 1082158542264721, 49785517156216897, 2412544311495241633, 122762020478952148177, 6542028190536528941425, 364254737003651267997985, 21146448814786605196994305

Offset: 1

Author

Paul D. Hanna, Aug 03 2012

Keywords

• nonn

Examples

			G.f.: A(x) = x + x^2 + x^3 + 49*x^4 + 721*x^5 + 17281*x^6 + 452065*x^7 +...
Let G(x) = A(A(A(A(x)))):
G(x) = x + 4*x^2 + 16*x^3 + 256*x^4 + 4864*x^5 + 111616*x^6 + 2983936*x^7 +...
such that G(x) = x + 3*x^2 + x*G(G(G(G(x)))):
G(G(G(G(x)))) = x + 16*x^2 + 256*x^3 + 4864*x^4 + 111616*x^5 + 2983936*x^6 +...
		

Crossrefs

Cf. A215116, A213009, A215115, A215119.

Programs

PARI

{a(n)=local(A=x+x^2,B=x+4*x^2);for(i=1,n+1,B=x+3*x^2+x*subst(B,x,subst(B,x,subst(B,x,B+x^2*O(x^n)))));
for(j=1, n+1, A=round((3*A+subst(B, x, serreverse(subst(A,x,subst(A,x,A+x^2*O(x^n))))))/4));; polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))

Formula

a(n) == 1 (mod 48).