A093962 - OEIS

%I #23 Aug 07 2024 22:39:13

%S 1,1,9,2,1,2,2,1,3,11,5,3,9,3,2,2,2,1,2,4,2,1,4,3,1,1,6,1,2,5,25,1,1,

%T 2,18,1,9,2,2,4,10,1,2,2,1,5,1,20,50,2,1,1,3,2,1,1,87,1,5,1,5,47,1,1,

%U 1,1,1,2,3,1,10,3,2,1,1,1,1,9,6,1,1,2,2,1,1,1,1,1,3,9,9,2,13,1,7,1,4,1,2,12

%N Continued fraction expansion of binomial(Pi,e) (A093961).

%C The increasing partial quotients are 1, 9, 11, 25, 50, 87, 514, 610, 647, 676, 2710, 10647, ...

%H Harry J. Smith, <a href="/A093962/b093962.txt">Table of n, a(n) for n = 0..4999</a>

%e 1.903568065729906338900833721... = 1 + 1/(1 + 1/(9 + 1/(2 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 17 2009

%t ContinuedFraction[ Binomial[Pi, E], 100]

%o (PARI) { allocatemem(932245000); default(realprecision, 5400); e=exp(1); x=contfrac(gamma(Pi+1)/(gamma(e+1)*gamma(Pi-e+1))); for (n=1, 5000, write("b093962.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Jun 17 2009

%o (Sage) continued_fraction_list( gamma(pi+1)/(gamma(e+1)*gamma(pi -e +1)), nterms=110) # _G. C. Greubel_, Dec 29 2021

%Y Cf. A093961 (decimal expansion).

%K cofr,nonn

%O 0,3

%A _Robert G. Wilson v_, Apr 20 2004

%E Offset changed by _Andrew Howroyd_, Aug 07 2024