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A002178
Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,1).
(Formerly M3216 N1302)
3
1, 4, 3, 32, 75, 216, 3577, 5888, 15741, 106300, 13486539, 9903168, 56280729661, 710986864, 265553865, 127626606592, 450185515446285, 1848730221900, 603652082270808125, 187926090380000, 9545933933230947
OFFSET
1,2
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}]; A002176[n_] := LCM @@ Table[Denominator[cn[n, k]], {k, 0, n}]; a[2] = 0; a[n_] := A002176[n]*cn[n, 1]; Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Oct 08 2013 *)
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, 1)
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Michael Somos
STATUS
approved