0,1

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

H. E. Salzer, Coefficients for mid-interval numerical integration with central differences, Phil. Mag., 36 (1945), 216-218.

T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 545.

T. D. Noe, Table of n, a(n) for n=0..100

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]

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]

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]

Cf. A002197.

See A000367, A006954, A008956 and A002671 for underlying sequences. [From Johannes W. Meijer (meijgia(AT)hotmail.com), Jan 27 2009]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)

Factor of the LS1[ -2,n] matrix coefficients in A160487.

(End)

Adjacent sequences: A002195 A002196 A002197 this_sequence A002199 A002200 A002201

Sequence in context: A151598 A003787 A002555 this_sequence A163576 A145408 A088616

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Maple program aligned with offset by Johannes W. Meijer (meijgia(AT)hotmail.com), May 15 2009