A136584 G.f. A(x) satisfies: 1+x = Sum_{n>=0} C(2^n,n) * x^n / A(x)^(2^n).

1, 1, 3, 31, 1327, 170211, 68333813, 89675072255, 397525147082217, 6103188627225900995, 331088233835064606501621, 64490029272314754165301653295, 45679131008965219349145151231118965

Offset: 0

Author

Paul D. Hanna, Jan 09 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 3*x^2 + 31*x^3 + 1327*x^4 + 170211*x^5 + ...
1 + x = Sum_{n>=0} C(2^n,n) * x^n * A(x)^(-2^n) =
(1 - x - 2x^2 - 26x^3 - 1264x^4 - 167480x^5 - 67988870x^6 -...) +
.2x*(1 - 2x - 3x^2 - 48x^3 - 2472x^4 - 332328x^5 -...) +
...6x^2*(1 - 4x - 2x^2 - 84x^3 - 4743x^4 - 654480x^5 -...) +
.......56x^3*(1 - 8x + 12x^2 - 152x^3 - 8810x^4 -...) +
..........1820x^4*(1 - 16x + 88x^2 - 496x^3 - 15044x^4 -...) +
..............201376x^5*(1 - 32x + 432x^2 - 3808x^3 -...) +
..................74974368x^6*(1 - 64x + 1888x^2 +...) + ...
		

Crossrefs

Cf. A014070 (C(2^n, n)).

Programs

PARI

{a(n)=local(A=[1,1]);if(n<0,0,if(n==0,1,for(i=0,n-1,A=concat(A,0); A[ #A]=Vec(sum(n=0,#A-1,log((1+2^n*x)/Ser(A))^n/n!))[ #A]);A[n+1]))}

Formula

G.f. A(x) satisfies: 1+x = Sum_{n>=0} log( (1 + 2^n*x)/A(x) )^n / n!.