A081791 Continued cotangent for sinh(1).

1, 12, 361, 6098638, 40523300374005, 2249947521757014011818803347, 23934989997298328927868650983263126279480229971908985849, 2858972935444266747494645602151444724302966656792002957565134720098726922500919331865545624811189334200411357440

Offset: 0

Author

Benoit Cloitre, Apr 10 2003

Keywords

• nonn

References

• D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

Crossrefs

Cf. A002666, A002667, A002668.

Programs

PARI

\p900
bn=vector(100);
bn[1]=sinh(1);
b(n)=if(n<0,0,bn[n]);
for(n=2,10,bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))));
a(n)=floor(b(n+1));

Formula

sinh(1) = cot(Sum_{n>=0} (-1)^n*acot(a(n))).

Let b(0) = sinh(1), b(n) = (b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1))) then a(n) = floor(b(n)).