|
%I #14 Feb 12 2019 23:27:04
%S 1,1,268,1073,15290,16363,48016,64379,176774,417927,594701,1607329,
%T 5416688,44940833,140239187,185180020,1066139287,4449737168,
%U 5515876455,81672007538,822235951835,903907959373,18900395139295,719118923252583,738019318391878
%N The continued fraction expansion of tanh(Pi) requires the computation of the pairs (p_n, q_n); sequence gives values of q_n.
%C a(2) = 268 explains the comment in A021085 that "The decimal expansion of Sum_{n>=1} floor(n * tanh(Pi))/10^n is the same as that of 1/81 for the first 268 decimal places [Borwein et al.]".
%D J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 13.
%H G. C. Greubel, <a href="/A190352/b190352.txt">Table of n, a(n) for n = 0..1920</a>
%F a(n) = A060402(n)*a(n-1) + a(n-2) for n >= 2. - _Nathaniel Johnston_, May 10 2011
%p lim:=50: with(numtheory): cfr := cfrac(tanh(Pi),lim+10,'quotients'): q[0]:=1:q[1]:=cfr[2]: printf("%d, %d, ", q[0], q[1]): for n from 2 to lim do q[n]:=cfr[n+1]*q[n-1]+q[n-2]: printf("%d, ",q[n]): od: # _Nathaniel Johnston_, May 10 2011
%t a[0] := 1; a[1] := 1; A060402:= ContinuedFraction[Tanh[Pi], 100];
%t a[n_]:= a[n] = A060402[[n + 1]]*a[n - 1] + a[n - 2]; Join[{1, 1}, Table[a[n], {n, 2, 75}]] (* _G. C. Greubel_, Apr 05 2018 *)
%Y Cf. A060402, A021085.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, May 09 2011
%E a(4)-a(24) from _Nathaniel Johnston_, May 10 2011
|
