A002179 Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,2). (Formerly M2921 N1172)

0, 1, 3, 12, 50, 27, 1323, -928, 1080, -48525, -3237113, -7587864, -31268252574, -770720657, -232936065, -179731134720, -542023437008852, -3212744374395, -926840515700222955, -389358194177500, -17858352159793110

Offset

2,3

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

Table of n, a(n) for n=2..22.

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-1]*cn[n-1, 2]; Table[a[n], {n, 2, 22}] (* 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, 2)

Crossrefs

Cf. A100640/A100641, A100620/A100621, A002176, A002177, A002178.

Sequence in context: A151176 A151177 A344419 * A224659 A034541 A180879

Adjacent sequences: A002176 A002177 A002178 * A002180 A002181 A002182

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

More terms from Michael Somos

Status

approved