%I A004273
%S A004273 0,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,
               49,
%T A004273 51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,
%U A004273 97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131
%N A004273 0 together with odd numbers.
%C A004273 Also continued fraction for tanh(1) (A073744 is decimal expansion). - 
               Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 07 2002
%C A004273 Lodumo_2 of A057427 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Apr 26 2009]
%C A004273 Contribution from Alexander R. Povolotsky and Paolo Lava, Oct 29 2009 
               (Start): From Inverse Symbolic Calculator Plus http://glooscap.cs.dal.ca:8087/
               advancedCalc Advanced lookup results for sum(2/(2^(n+1))/GAMMA(n+1/
               2)*Pi^(1/2),n = 1 .. infinity) Transform Searched for Description 
               K*1 1.4106861346424479976908247 Sum(1/prod(A004273(k),k=1..n),n=1..inf) 
               Below are two Maple programs, developed by Paolo Lava confirming 
               that indeed sum(2/(2^(n+1))/GAMMA(n+1/2)*Pi^(1/2),n = 1 .. infinity) 
               = Sum(1/prod(A004273(k),k=1..n),n=1..inf). To reiterate, it appears 
               that indeed the two formulae practically give the same result!
%C A004273 Maple program for Sum(1/prod(A004273(k),k=1..n),n=1..inf)is:
%C A004273 Formula1:=proc(i) local a,k,n,t; for n from 1 by 1 to i do a:=add(1/product(2*t-1,
               t=1..k),k=1..n); print(evalf(a,600)); od; end: Formula1(10000);
%C A004273 Maple program for the formula using GAMMA function is:
%C A004273 Formula2:=proc(i) local a,k,n; for n from 1 by 1 to i do a:=add(2/(2^(k+1))/
               GAMMA(k+1/2)*Pi^(1/2),k=1..n); print(evalf(a,600)); od; end: Formula2(10000); 
               Both programs were run up to 10.000 iterations showing 599 decimal 
               digits.
%C A004273 The result in both cases is: 1.41068613464244799769082471141911504132347\
%C A004273 862562519219772463946816478179849039792711540922477861164014728970035593\
%C A004273 291934262239437689612130677631195100435759045028697694516138268925799622\
%C A004273 506579245758816483482960481133594351367886637443783678748021144275108269\
%C A004273 196477247936726250874958337834244668843998292968423370781551842367181745\
%C A004273 798283956182034092760339072832832252093637885530596099628134118249573271\
%C A004273 812709090115944540248304702415273410481321124791326873921867111910022107\
%C A004273 760939194553035779605182699929996414630218895949183315671171755021724947\
%C A004273 333256207314724810499711097293803256333031250513313069 (End of the contribution 
               from Alexander R. Povolotsky and Paolo Lava)
%F A004273 a(n)=2*n-[(n+2) mod (n+1)], with n>=0 - Paolo P. Lava (ppl(AT)spl.at), 
               Aug 29 2007
%F A004273 G.f.: x*(1+x)/(-1+x)^2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 18 2007
%F A004273 a(n)=lod_2(A057427(n)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Apr 26 2009]
%p A004273 a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-1]+2 od: seq(a[n], n=0..66); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
%Y A004273 Sequence in context: A165747 A053229 A157142 this_sequence A005408 A144396 
               A060747
%Y A004273 Adjacent sequences: A004270 A004271 A004272 this_sequence A004274 A004275 
               A004276
%K A004273 easy,nonn
%O A004273 0,3
%A A004273 N. J. A. Sloane (njas(AT)research.att.com).