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A081793 Continued cotangent for tanh(1). 0
0, 1, 7, 135, 35445, 44465908998, 5112887721516309845621, 75234509360529020708450352828794956245887456, 5786575206590910267083400178061771765781639734324927167565054640197289842752623499343753 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..8.

FORMULA

tanh(1)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=tanh(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) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=tanh(1); ?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: A143181 A183478 A292395 * A296595 A210028 A243684

Adjacent sequences:  A081790 A081791 A081792 * A081794 A081795 A081796

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 10 2003

STATUS

approved

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Last modified September 21 05:55 EDT 2020. Contains 337267 sequences. (Running on oeis4.)