A203014 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (2*A(x)^n - 1)^n.

1, 1, 3, 15, 93, 655, 5025, 40995, 350665, 3116083, 28588541, 269632839, 2606374433, 25766661303, 260133432037, 2679336234403, 28138284922321, 301224023801747, 3286962740398689, 36567211855460123, 414883492490364865, 4802747139352783619, 56754591674540964917

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

 G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 93*x^4 + 655*x^5 + 5025*x^6 +...
where the g.f. satisfies following series identity:
A(x) = 1 + (2*A(x)-1)*x + (2*A(x)^2-1)^2*x^2 + (2*A(x)^3-1)^3*x^3 + (2*A(x)^4-1)^4*x^4 +...
A(x) = 1/(1+x) + 2*x*A(x)/(1+x*A(x))^2 + 2^2*x^2*A(x)^4/(1+x*A(x)^2)^3 + 2^3*x^3*A(x)^9/(1+x*A(x)^3)^4 + 2^4*x^4*A(x)^16/(1+x*A(x)^4)^5 +...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, (2*A^k-1+x*O(x^n))^k*x^k)); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, 2^k*A^(k^2)*x^k/(1+A^k*x+x*O(x^n))^(k+1) )); polcoeff(A, n)}

Crossrefs

Cf. A203000.

Sequence in context: A368966 A074539 A103210 * A060066 A206177 A366638

Adjacent sequences: A203011 A203012 A203013 * A203015 A203016 A203017

Keyword

nonn

Author

Paul D. Hanna, Dec 27 2011

Status

approved