A002548 Denominators of coefficients for numerical differentiation. (Formerly M4822 N2063)

1, 1, 12, 6, 180, 10, 560, 1260, 12600, 1260, 166320, 13860, 2522520, 2702700, 2882880, 360360, 110270160, 2042040, 775975200, 162954792, 56904848, 2586584, 1427794368, 892371480, 116008292400, 120470149800, 1124388064800

Offset

2,3

Comments

Denominator of 1 - 2*HarmonicNumber(n-1)/n. - Eric W. Weisstein, Apr 15 2004

Denominator of u(n) = sum( k=1, n-1, 1/(k(n-k)) ) (u(n) is asymptotic to 2*log(n)/n). - Benoit Cloitre, Apr 12 2003; corrected by Istvan Mezo, Oct 29 2012

Expected area of the convex hull of n points picked at random inside a triangle with unit area. - Eric W. Weisstein, Apr 15 2004

References

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 = 2..250

W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).

W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables) [Annotated scanned copy]

A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924.

A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924. [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Triangle Point Picking

Eric Weisstein's World of Mathematics, Simplex Simplex Picking

Index entries for sequences related to the Josephus Problem

Formula

G.f.: (-log(1-x))^2 (for fractions A002547(n)/A002548(n)).

A002547(n)/a(n) = 2*Stirling_1(n+2, 2)(-1)^n/(n+2)!.

Example

0, 0, 1/12, 1/6, 43/180, 3/10, 197/560, 499/1260, 5471/12600, ...

Maple

seq(denom(Stirling1(j+2, 2)/(j+2)!*2!*(-1)^j), j=0..50);

Mathematica

Table[Denominator[1 - 2*HarmonicNumber[n - 1]/n], {n, 2, 30}] (* Wesley Ivan Hurt, Mar 24 2014 *)

Crossrefs

Cf. A002547, A093762.

Sequence in context: A177690 A038332 A093763 * A363151 A359632 A364135

Adjacent sequences: A002545 A002546 A002547 * A002549 A002550 A002551

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms, GF, formula, Maple code from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 16 2007

Status

approved