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 A002177 Numerators of Cotesian numbers (not in lowest terms): A002176(n)*C(n,0). (Formerly M4364 N1829) 10
 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; text; internal format)
 OFFSET 1,4 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). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..100 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] 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}] (* Jean-François 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) ncn(n) = denominator(cn(n)) * cn(n); (PARI) nk(n, k) = if(k<0 || k>n, 0, ncn(n)[ k+1 ]); (PARI) A002177(n) = nk(n, 0); CROSSREFS Cf. A100640/A100641, A100620/A100621, A002176-A002179. Sequence in context: A067889 A190821 A100620 * A225279 A192755 A141193 Adjacent sequences: A002174 A002175 A002176 * A002178 A002179 A002180 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane EXTENSIONS More terms from Michael Somos STATUS approved

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Last modified February 27 19:38 EST 2024. Contains 370378 sequences. (Running on oeis4.)