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A002198
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Denominators of coefficients for numerical integration.
(Formerly M5178 N2250)
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6
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24, 5760, 967680, 464486400, 122624409600, 2678117105664000, 64274810535936000, 149852129706639360000, 669659197233029971968000, 8839501403475995629977600000, 4879404774718749587747635200000
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OFFSET
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0,1
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COMMENTS
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The denominators of these coefficients for numerical integration are a combination of the Bernoulli numbers B{2k}, the central factorial numbers A008956(n, k) and the factor 4^n*(2*n+1)!. - Johannes W. Meijer, Jan 27 2009
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REFERENCES
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H. E. Salzer, Coefficients for mid-interval numerical integration with central differences, Phil. Mag., 36 (1945), 216-218.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = denominator(Sum_{k=1..n+1}((1-2^(2*k-1))*(-1)^k*(B_{2k}/(2*k))*A008956(n, n+1-k)) / (2*4^(n)*(2*n+1)!)) for n >= 0. - Johannes W. Meijer, Jan 27 2009
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MAPLE
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nmax:=10: for n from 0 to nmax do A008956(n, 0) := 1: A008956(n, n) := (doublefactorial(2*n-1))^2 od: for n from 1 to nmax do for k from 1 to n-1 do A008956(n, k) := (2*n-1)^2*A008956(n-1, k-1) + A008956(n-1, k) od: od:
for n from 0 to nmax do Delta(n) := add((1-2^(2*k1-1)) * (-1)^k1 * (bernoulli(2*k1)/(2*k1)) * A008956(n, n+1-k1), k1=1..n+1) / (2*4^(n)*(2*n+1)!) end do: a:=n-> denom (Delta(n)): seq(a(n), n=0..nmax); # Johannes W. Meijer, Jan 27 2009, Revised Sep 21 2012
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CROSSREFS
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Factor of the LS1[ -2,n] matrix coefficients in A160487.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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