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A002548
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Denominators of coefficients for numerical differentiation.
(Formerly M4822 N2063)
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6
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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; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| 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
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REFERENCES
| 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.
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).
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LINKS
| Eric Weisstein's World of Mathematics, Triangle Point Picking
Eric Weisstein's World of Mathematics, Simplex Simplex Picking
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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)!
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EXAMPLE
| 0, 0, 1/12, 1/6, 43/180, 3/10, 197/560, 499/1260, 5471/12600, ...
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MAPLE
| with(combinat): seq(denom(stirling1(j+2, 2)/(j+2)!*2!*(-1)^j), j=0..50);
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CROSSREFS
| Cf. A002547, A093762.
Sequence in context: A177690 A038332 A093763 * A038598 A206423 A038333
Adjacent sequences: A002545 A002546 A002547 * A002549 A002550 A002551
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KEYWORD
| nonn,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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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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