login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A067889 A190821 A100620 * A225279 A192755 A141193
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Michael Somos
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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