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A002548 Denominators of coefficients for numerical differentiation.
(Formerly M4822 N2063)
+0
6
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 (list; graph; listen)
OFFSET

2,3

COMMENT

Denominator of 1-2HarmonicNumber[n]/(n+1). - Eric Weisstein (eric(AT)weisstein.com), Apr 15, 2004

Denominator of u(n)=sum(k=1,n,1/k/(n-k)) (u(n) is asymptotic to 2*log(n)/n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003

Expected area of the convex hull of n points picked at random inside a triangle with unit area. - Eric Weisstein (eric(AT)weisstein.com), Apr 15, 2004

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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).

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

LINKS

Eric Weisstein's World of Mathematics, Triangle Point Picking

Eric Weisstein's World of Mathematics, Simplex Simplex Picking

FORMULA

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

A002547(n)/A002548(n)=2 stirling1(n+2, n)(-1)^n/(n+2)!

EXAMPLE

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

MAPLE

with(combinat): seq(denom(stirling1(j+2, 2)/(j+2)!*2!*(-1)^j), j=0..50);

CROSSREFS

Cf. A002547, A093762.

Sequence in context: A119870 A038332 A093763 this_sequence A038598 A038333 A090438

Adjacent sequences: A002545 A002546 A002547 this_sequence A002549 A002550 A002551

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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 (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 16 2007

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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