A352798 - OEIS

%I #56 Jul 06 2022 19:36:18

%S 1,-10,330,-21960,2551640,-461930274,120572270007,-42930583856160,

%T 20008932768992430,-11825788272679695050,8643081649999714376976,

%U -7654102744143874729100040,8076084821027629176909996013,-10010473694454865001226770534530,14402393216408406872433735669683370

%N a(n) = 1/(cf[0;n,n,n,...,n] - cf[0;n,n,...,n]) where the first continued fraction has n+1 terms and the second has n terms.

%F a(n) = A084844(n)*A084845(n)*(-1)^(n+1).

%e a(2) = -10 because the two continued fractions are cf[0;2,2] = 0 + 1/(2 + 1/2) = 2/5 and cf[0;2] = 0 + 1/2 = 1/2 and the reciprocal of their difference is 1/(2/5 - 1/2) = -10.

%e a(3) = 330 because the two continued fractions are cf[0;3,3,3] = 0 + 1/(3 + 1/(3 + 1/3)) = 10/33 and cf[0;3,3] = 0 + 1/(3 + 1/3) = 3/10, and 1/(10/33 - 3/10) = 330.

%p a:= n-> (f-> -(-1)^n*f(n,n)*f(n+1,n))(combinat[fibonacci]):

%p seq(a(n), n=1..15);  # _Alois P. Heinz_, Jul 06 2022

%o (PARI) a(n) = (-1)^(n+1) * vecprod(Vec(lift(Mod('x,'x^2-n*'x-1)^(n+1)))); \\ _Kevin Ryde_, Apr 18 2022

%o (Python)

%o from sympy.ntheory.continued_fraction import continued_fraction_reduce

%o def A352798(n): return int(1/(continued_fraction_reduce([0]+[n]*n)-continued_fraction_reduce([0]+[n]*(n-1)))) # _Chai Wah Wu_, Jul 06 2022

%Y Cf. A084844, A084845.

%K sign,easy

%O 1,2

%A _Sebastian F. Orellana_, Apr 03 2022

%E More terms from _Kevin Ryde_, Apr 18 2022