A081791 Continued cotangent for sinh(1).

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

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..7.

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)).

Prog

(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));

Crossrefs

Cf. A002666, A002667, A002668.

Sequence in context: A012385 A012430 A012632 * A166183 A218310 A268550

Adjacent sequences: A081788 A081789 A081790 * A081792 A081793 A081794

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Status

approved