A217041 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (A(x)^n + 1/A(x)^n)^n.

1, 2, 4, 12, 88, 624, 4112, 32912, 293280, 2576896, 23669376, 233756544, 2372829696, 24679378432, 268444154624, 3026232635648, 35050705650176, 420323656792064, 5218917552457728, 66738035973859328, 880566524142424064, 11998061103578816512, 168314109964357738496

Offset

0,2

Links

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

Formula

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

Example

 G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 88*x^4 + 624*x^5 + 4112*x^6 +...
where
A(x) = 1 + x*(A(x)+1/A(x)) + x^2*(A(x)^2+1/A(x)^2)^2 + x^3*(A(x)^3+1/A(x)^3)^3 + x^4*(A(x)^4+1/A(x)^4)^4 +...
A(x)+1/A(x) = 2 + 4*x^2 + 8*x^3 + 32*x^4 + 304*x^5 + 2160*x^6 +...
(A(x)^2+1/A(x)^2)^2 = 4 + 64*x^2 + 128*x^3 + 832*x^4 + 6144*x^5 +...
(A(x)^3+1/A(x)^3)^3 = 8 + 432*x^2 + 864*x^3 + 12384*x^4 + 68544*x^5 +...
(A(x)^4+1/A(x)^4)^4 = 16 + 2048*x^2 + 4096*x^3 + 124928*x^4 + 589824*x^5 +...

Prog

 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=sum(m=0, n, x^m*(A^m+1/A^m)^m)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A203000, A212961, A186999.

Sequence in context: A217757 A053631 A319634 * A120618 A259048 A228809

Adjacent sequences: A217038 A217039 A217040 * A217042 A217043 A217044

Keyword

nonn

Author

Paul D. Hanna, Sep 26 2012

Status

approved