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A002176
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a(n) = LCM of denominators of Cotesian numbers {C(n,k), 0 <= k <= n}.
(Formerly M1569 N0612)
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18
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2, 6, 8, 90, 288, 840, 17280, 28350, 89600, 598752, 87091200, 63063000, 402361344000, 5003856000, 2066448384, 976924698750, 3766102179840000, 15209113920000, 5377993912811520000, 1646485441080480, 89903156428800000
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OFFSET
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1,1
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COMMENTS
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See A100640 for definition of C(n,k).
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 886.
Louis Brand, Differential and Difference Equations, 1966, p. 612.
W. W. Johnson, On Cotesian numbers: their history, computation and values to n=20, Quart. J. Pure Appl. Math., 46 (1914), 52-65.
Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
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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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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MAPLE
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Define C(n, k) as in A100640, then: A002176:=proc(n) local t1, k; t1:=1; for k from 0 to n do t1:=lcm(t1, denom(C(n, k))); od: t1; end;
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MATHEMATICA
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cn[n_, 0] := Sum[ n^j*StirlingS1[n, j]/(j+1), {j, 1, n+1}]/n!; cn[n_, n_] := cn[n, 0]; cn[n_, k_] := 1/n!*Binomial[n, k]*Sum[n^(j+m)*StirlingS1[k, j]* StirlingS1[n-k, m]/((m+1)*Binomial[j+m+1, m+1]), {m, 1, n}, {j, 1, k+1}]; a[n_] := LCM @@ Table[ Denominator[cn[n, k]], {k, 0, n}]; Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Oct 25 2011 *)
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PROG
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(PARI) cn(n)= mattranspose(matinverseimage( matrix(n+1, n+1, k, m, (m-1)^(k-1)), matrix(n+1, 1, k, m, n^(k-1)/k)))[ 1, ] \\ vector of quadrature formula coefficients via matrix solution
(PARI) A002176(n)= denominator(cn(n))
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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