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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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]

Crossrefs

Cf. A100640/A100641, A100620/A100621, A002176-A002179.

Programs

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 *)

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);

Extensions

More terms from Michael Somos