Search: id:A069955
Results 1-1 of 1 results found.

%I A069955
%S A069955 1,3,45,175,11025,43659,693693,2760615,703956825,2807136475,
%T A069955 44801898141,178837328943,11425718238025,45635265151875,
%U A069955 729232910488125,2913690606794775,2980705490751054825
%N A069955 Let W(n)=Prod(k=1,n,1-1/4k^2), the partial Wallis product ( lim n -> 
               infinity W(n)=2/Pi ); then a(n)=numerator(W(n)).
%C A069955 Equivalently, denominators in partial products of the following approximation 
               to Pi: Pi = Product_{n >= 1} 4*n^2/(4*n^2-1). Numerators are in A056982.
%D A069955 O. J. Farrell and B. Ross, Solved Problems in Analysis, Dover, NY, 1971; 
               p. 77.
%H A069955 B. Gourevitch, <a href="http://www.pi314.net">L'univers de Pi</a>
%F A069955 a(n)= numerator(W(n)) with W(n)=(2*n)!*(2*n+1)!/((2^n)*n!)^4.
%F A069955 W(n)=(2*n+1)*(binomial(2*n,n)/2^(2*n))^2 = (2*n+1)*(A001790(n)/A046161(n))^2 
               in lowest terms.
%Y A069955 Not the same as A001902(n).
%Y A069955 Cf. A056982.
%Y A069955 W(n)=(3/4)*(A120995(n)/A120994(n)), n>=1.
%Y A069955 Sequence in context: A071968 A093585 A062270 this_sequence A062346 A002682 
               A073595
%Y A069955 Adjacent sequences: A069952 A069953 A069954 this_sequence A069956 A069957 
               A069958
%K A069955 easy,frac,nonn
%O A069955 0,2
%A A069955 Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2002

Search completed in 0.001 seconds