%I A097301
%S A097301 1,1,2,3,3360,995040,39916800,656924748480,1214047650816000,169382556838010880,
%T A097301 15749593891765493760000,4054844479616799289344000,34017686450062663131463680000,
%U A097301 11402327189708082115897599590400000,189528830020089532044244068728832000000
%V A097301 1,-1,2,-3,3360,-995040,39916800,-656924748480,1214047650816000,-169382556838010880,
%W A097301 15749593891765493760000,-4054844479616799289344000,34017686450062663131463680000,
%X A097301 -11402327189708082115897599590400000,189528830020089532044244068728832000000
%N A097301 Numerators of rationals used in the Euler-Maclaurin type derivation of 
               Stirling's formula for N!.
%C A097301 Denominators are given in A097302.
%C A097301 The e.g.f. sum( A(2*n+1)*(x^(2*n+1))/(2*n+1)!,n=0..infinity) appears 
               in the Stirling-formula derivation for N! with x=1/N in the exponent 
               and the formula for A(2*n+1):=a(n)/A097302(n), n>=0, is given below. 
               For Stirling's formula see A001163 and A001164.
%C A097301 The rationals A(2*n+1) = B(n):= (2*n)!*Bernoulli(2*(n+1))/(2*(n+1)) = 
               a(n)/A097304(n) with A(2*n):=0 are the logarithmic transform of the 
               rational sequence {A001163(n)/A001164(n)} (inverse of the sequence 
               transform EXP)
%D A097301 Julian Havil, Gamma, Exploring Euler's Constant, Princeton University 
               Press, Princeton and Oxford, 2003, p. 87.
%H A097301 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A097301.text">
               More terms and comments</a>.
%H A097301 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A097301 a(n)=numerator(B(n)) with B(n):=Bernoulli(2*n+2)*(2*n)!/(2*n+2) and Bernoulli(n)= 
               A027641(n)/A027642(n).
%Y A097301 Sequence in context: A066848 A125612 A038104 this_sequence A020345 A085943 
               A068661
%Y A097301 Adjacent sequences: A097298 A097299 A097300 this_sequence A097302 A097303 
               A097304
%K A097301 sign,frac,easy
%O A097301 0,3
%A A097301 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Aug 13 2004