Search: id:A046126
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%I A046126
%S A046126 1,3,3,15,45,315,1575,14175,99225,1091475,9823275,127702575,
%T A046126 1404728325,21070924875,273922023375,4656674397375,69850115960625,
%U A046126 1327152203251875,22561587455281875,473793336560919375
%V A046126 1,3,-3,-15,45,315,-1575,-14175,99225,1091475,-9823275,-127702575,
%W A046126 1404728325,21070924875,-273922023375,-4656674397375,69850115960625,
%X A046126 1327152203251875,-22561587455281875,-473793336560919375
%N A046126 Denominators q[ n ] of convergents to Stern's non-simple continued fraction 
               for Pi/2.
%H A046126 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Pi.html">Link to a section of The World of Mathematics.</a>
%H A046126 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PiContinuedFraction.html">Link to a section of The World of Mathematics.</
               a>
%H A046126 <a href="Sindx_St.html#Stern">Index entries for sequences related to 
               Stern's sequences</a>
%F A046126 E.g.f.: exp(asinh(x))((1+x)/(1+x^2)+(2-x+x^2)/(1+x^2)^(3/2))-2. - Michael 
               Somos Mar 11 2004
%t A046126 b[ n_ ] := 2-(-1)^n; a[ 1 ] := -1; a[ n_Integer?EvenQ ] := -n(n+1); a[ 
               n_Integer?OddQ ] := -(n-2)(n-1); then use the standard algorithm 
               to get p[ n ]/q[ n ].
%o A046126 (PARI) a(n)=if(n<0,0,prod(k=1,n,if(k%2,k+2,1-k)))
%o A046126 (PARI) {a(n)=local(A); if(n<0, 0, A=matrix(2,n+1); for(k=0, n, A[2, k+1]=if(k%2, 
               3, 1); A[1, k+1]=if(k<2, (-1)^k, if(k%2, -(k-2)*(k-1), -k*(k+1)))); 
               contfracpnqn(A)[2,1])} /* Michael Somos Jul 15 2003 */
%Y A046126 Numerators p[ n ] are (-1)^[n/2]*A001900(n). See also A013069.
%Y A046126 Cf. A079484.
%Y A046126 Sequence in context: A046983 A067655 A049606 this_sequence A143257 A089403 
               A111674
%Y A046126 Adjacent sequences: A046123 A046124 A046125 this_sequence A046127 A046128 
               A046129
%K A046126 sign,frac
%O A046126 0,2
%A A046126 Eric Weisstein (eric(AT)weisstein.com)

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