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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..21.

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-Fran├žois 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)

CROSSREFS

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

Sequence in context: A064081 A211364 A099438 * A013558 A161000 A220363

Adjacent sequences:  A002175 A002176 A002177 * A002179 A002180 A002181

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Michael Somos

STATUS

approved

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Last modified December 16 01:43 EST 2019. Contains 330013 sequences. (Running on oeis4.)