A122939 G.f. A(x) satisfies: A(x+x^2) = A(x)^2/(1+x)^2.

1, 2, 3, 6, 17, 70, 390, 2776, 24042, 244864, 2862185, 37715474, 552685976, 8910951840, 156709821779, 2984589501562, 61188398397436, 1343410717573876, 31445844702847347, 781689483100388326, 20564696601659697997

Offset: 0

Author

Paul D. Hanna, Sep 21 2006

Keywords

• nonn

Comments

Self-convolution of A122938. See A122888 for the table of self-compositions of x+x^2.

Examples

			G.f.: A(x) = (1 + x) * (1 + x+x^2)^(1/2) * (1 + x+2x^2+2x^3+x^4)^(1/4) * (1 + x+3x^2+6x^3+9x^4+10x^5+8x^6+4x^7+x^8)^(1/8) *...
		

Crossrefs

Cf. A122938 (square-root), A122888 (table).

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n)); for(i=0,n,A=-A+2*(1+x)*sqrt(subst(A,x,x+x^2+x*O(x^n))));polcoeff(A,n)}

Formula

G.f.: A(x) = Product_{n>=0} (1 + F_n(x) )^(1/2^n) where F_0(x)=x, F_{n+1}(x)=F_n(x+x^2); a product that involves the n-th self-compositions of x+x^2.