A002177 Numerators of Cotesian numbers (not in lowest terms): A002176(n)*C(n,0). (Formerly M4364 N1829)

1, 1, 1, 7, 19, 41, 751, 989, 2857, 16067, 2171465, 1364651, 8181904909, 90241897, 35310023, 15043611773, 55294720874657, 203732352169, 69028763155644023, 19470140241329, 1022779523247467, 396760150748100749

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