Search: id:A144846
Results 1-1 of 1 results found.

%I A144846
%S A144846 0,1,1,7,5,3,87,35,63,5,2047,105,819,45,35,78655,8085,15939,
%T A144846 7425,1925,63,4439935,57057,225225,211497,115115,2457,231,
%U A144846 344674687,4429425,17486469,8217495,9003995,200655,24255,429
%V A144846 0,1,-1,7,-5,3,87,-35,63,-5,2047,-105,819,-45,35,78655,-8085,15939,
%W A144846 -7425,1925,-63,4439935,-57057,225225,-211497,115115,-2457,231,
%X A144846 344674687,-4429425,17486469,-8217495,9003995,-200655,24255,-429
%N A144846 Numerators of triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) is 
               the coefficient of x^(2k+1) in polynomial u_n(x), used to approximate 
               x->sin(Pi*x)/Pi.
%C A144846 All even coefficients of u_n are 0. Sum_{k=0..n} T(n,k) = 0. 1/u(n)(1/
               2) is an approximation to Pi.
%F A144846 See program.
%e A144846 0, 1/2, -1/2, 7/8, -5/4, 3/8, 87/88, -35/22, 63/88, -5/44, 2047/2048, 
               -105/64, 819/1024, -45/256, 35/2048, 78655/78656, -8085/4916, 15939/
               19664, -7425/39328, 1925/78656, -63/39328 ... = A144846/A144847
%e A144846 As triangle:
%e A144846 0
%e A144846 1/2, -1/2
%e A144846 7/8, -5/4, 3/8
%e A144846 87/88, -35/22, 63/88, -5/44
%p A144846 u:= proc(n) option remember; local f,i,x; f:= unapply (simplify (sum 
               ('cat (a||(2*i+1)) *x^(2*i+1)', 'i'=0..n) ), x); unapply (subs (solve 
               ({f(1)=0, seq((D@@i)(f)(1)=`if`(i=1,-1,-(D@@i)(f)(0)), i=1..n)}, 
               {seq (cat (a||(2*i+1)), i=0..n)}), sum ('cat (a||(2*i+1)) *x^(2*i+1)', 
               'i'=0..n) ), x); end: T:= (n,k)-> coeff (u(n)(x), x, 2*k+1): seq 
               (seq (numer (T(n,k)), k=0..n), n=0..9);
%Y A144846 Denominators of T(n, k): A144847. Diagonal gives: (-1)^n A001790(n) for 
               n>1.
%Y A144846 Sequence in context: A155816 A093824 A019935 this_sequence A090289 A160670 
               A109863
%Y A144846 Adjacent sequences: A144843 A144844 A144845 this_sequence A144847 A144848 
               A144849
%K A144846 frac,sign,tabl
%O A144846 0,4
%A A144846 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 22 2008

Search completed in 0.001 seconds