A343439 G.f.: 1 + 2^0*x/(1 + 2^1*x/(1 + 2^2*x/(1 + 2^3*x/(1 + 2^4*x/(1 + ...))))).

1, 1, -2, 12, -136, 2736, -99616, 6810816, -900563072, 234247256832, -120883821425152, 124271556482829312, -255006726559759042560, 1045529090595650037657600, -8569159507007490469146992640, 140431398588497630920722150113280, -4602217897540461023955069241211781120

Offset: 0

Author

Seiichi Manyama, Apr 15 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A015083, A168491, A216966.

Programs

PARI

a(n) = my(A=1+O(x)); for(i=1, n, A=1+2^(n-i)*x/A); polcoef(A, n);

PARI

a(n) = if(n<2, 1, -sum(k=1, n-1, 2^k*a(k)*a(n-k)));

Formula

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

G.f.: 1/(Sum_{k>=0} A015083(k) * (-x)^k).

a(0) = a(1) = 1 and a(n) = -Sum_{k=1..n-1} 2^k*a(k)*a(n-k) for n > 1.

a(n) = (-2)^(n-1) * A015083(n-1) for n > 0.