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A002177
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Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,0).
(Formerly M4364 N1829)
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10
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1, 1, 1, 7, 19, 41, 751, 989, 2857, 16067, 2171465, 1364651, 8181904909, 90241897, 35310023, 15043611773, 55294720874657, 203732352169, 69028763155644023, 19470140241329, 1022779523247467, 396760150748100749
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| W. W. Johnson, On Cotesian numbers: their history, computation and values to n=20, Quart. J. Pure Appl. Math., 46 (1914), 52-65.
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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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_] := cn[n, 0]*LCM @@ Table[ Denominator[cn[n, k]], {k, 0, n}]; Table[a[n], {n, 1, 22}] (* From Jean-François Alcover, Oct 25 2011 *)
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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) ncn(n)= denominator(cn(n))*cn(n); nk(n, k)= if(k<0|k>n, 0, ncn(n)[ k+1 ]); A002177(n)= nk(n, 0)
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CROSSREFS
| Cf. A100640/A100641, A100620/A100621, A002176-A002179.
Sequence in context: A067889 A190821 A100620 * A192755 A141193 A104163
Adjacent sequences: A002174 A002175 A002176 * A002178 A002179 A002180
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Michael Somos
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