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%I A002198 M5178 N2250
%S A002198 24,5760,967680,464486400,122624409600,2678117105664000,
%T A002198 64274810535936000,149852129706639360000,669659197233029971968000
%N A002198 Denominators of coefficients for numerical integration.
%C A002198 The denominators of these coefficients for numerical integration are 
               a combination of the Bernoulli numbers B{_2k}, the central factorial 
               numbers 4^(k)t(2n+1,2n+1-2k) and the factor 4^n*(2*n+1)!. [From Johannes 
               W. Meijer (meijgia(AT)hotmail.com), Jan 27 2009]
%D A002198 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002198 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002198 H. E. Salzer, Coefficients for mid-interval numerical integration with 
               central differences, Phil. Mag., 36 (1945), 216-218.
%D A002198 T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, 
               Vol. 2, Engelmann, Leipzig, 1880, p. 545.
%H A002198 T. D. Noe, <a href="b002198.txt">Table of n, a(n) for n=0..100</a>
%F A002198 a(n) = denominator of sum((1-2^(2*k-1))* (-1)^(k)*(B_{2k}/(2*k))*4^(n-k)*t(2*n-1,
               2*k-1),k=1..n) /(2*4^(n-1)*(2*n-1)!) for n = 0,1,2,3,... [From Johannes 
               W. Meijer (meijgia(AT)hotmail.com), Jan 27 2009]
%e A002198 a(2) = denom(((1-2^1)*(-1)*((1/6)/2)*(9) + (1-2^3)*(1)*((-1/30)/4)*(10) 
               + (1-2^5)*(-1)*((1/42)/6)*(1))/(2*4^2*5!)) so a(2) = 967680. [From 
               Johannes W. Meijer (meijgia(AT)hotmail.com), Jan 27 2009]
%p A002198 nmax:=9: jn:=nmax: im:=nmax: for n from 1 to nmax do for i from 2 to 
               im do cfn2[i,1]:=0 end do: for j from 1 to jn do cfn2[1,j]:=1 end 
               do: for j from 2 to jn do for i from 2 to im do cfn2[i,j]:= cfn2[i,
               j-1] + cfn2[i-1,j-1]*(2*j-3)^2 end do end do: Delta[n-1]:=sum((1-2^(2*k-1))* 
               (-1)^(n+1)*(-bernoulli(2*k)/(2*k))*(-1)^(k+n)*cfn2[n-k+1,n],k=1..n) 
               /(2*4^(n-1)*(2*n-1)!) end do: a:=n-> denom(Delta[n]): seq(a(n),n=0..nmax-1); 
               [From Johannes W. Meijer (meijgia(AT)hotmail.com), Jan 27 2009]
%Y A002198 Cf. A002197.
%Y A002198 See A000367, A006954, A008956 and A002671 for underlying sequences. [From 
               Johannes W. Meijer (meijgia(AT)hotmail.com), Jan 27 2009]
%Y A002198 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A002198 Factor of the LS1[ -2,n] matrix coefficients in A160487.
%Y A002198 (End)
%Y A002198 Sequence in context: A151598 A003787 A002555 this_sequence A163576 A145408 
               A088616
%Y A002198 Adjacent sequences: A002195 A002196 A002197 this_sequence A002199 A002200 
               A002201
%K A002198 nonn
%O A002198 0,1
%A A002198 N. J. A. Sloane (njas(AT)research.att.com).
%E A002198 Maple program aligned with offset by Johannes W. Meijer (meijgia(AT)hotmail.com), 
               May 15 2009

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