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A002176 a(n) = LCM of denominators of Cotesian numbers {C(n,k), 0 <= k <= n}.
(Formerly M1569 N0612)
18
2, 6, 8, 90, 288, 840, 17280, 28350, 89600, 598752, 87091200, 63063000, 402361344000, 5003856000, 2066448384, 976924698750, 3766102179840000, 15209113920000, 5377993912811520000, 1646485441080480, 89903156428800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A100640 for definition of C(n,k).

REFERENCES

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).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

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].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 886.

W. M. Johnson, On Cotesian numbers: their history, computation and values to n=20, Quart. J. Pure Appl. Math., 46 (1914), 52-65. [Annotated scanned copy]

MAPLE

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;

MATHEMATICA

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-Fran├žois Alcover, Oct 25 2011 *)

PROG

(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))

CROSSREFS

Cf. A002177-A002179, A100620, A100621, A100640, A100641, A100642.

Sequence in context: A075998 A007849 A100621 * A124675 A279258 A120709

Adjacent sequences:  A002173 A002174 A002175 * A002177 A002178 A002179

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms and references from Michael Somos

STATUS

approved

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Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)