A122894 Coefficient of x^(2^(n-1)) in the n-th self-composition of (x+x^2) for n>=1.

1, 2, 9, 258, 293685, 531124770570, 2439717292075827330588969, 72554628124279239546273779187960042205300343234178

Offset: 1

Author

Paul D. Hanna, Sep 19 2006

Keywords

• nonn

Comments

Originated by Ralf Stephan in A092123 as the 2^(n-1)th coefficient in the expansion of P(0)=x, P(n+1)=P(n)*[1+P(n)] (equivalent definition). Next term is too large to include.

Examples

			a(1) = 1 = [x^1] (x + x^2).
a(2) = 2 = [x^2] (x + 2*x^2 + 2*x^3 + x^4).
a(3) = 9 = [x^4] (x + 3*x^2 + 6*x^3 + 9*x^4 + 10*x^5 + 8*x^6 + 4*x^7 + x^8).
		

Crossrefs

Cf. A092123, A122893; A122888.

Programs

PARI

{a(n)=local(F=x+x^2, G=x+x*O(x^(2^(n-1)))); if(n<1, 0, for(i=1, n, G=subst(F, x, G)); return(polcoeff(G, 2^(n-1), x)))}