Search: id:A002548
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%I A002548 M4822 N2063
%S A002548 1,1,12,6,180,10,560,1260,12600,1260,166320,13860,2522520,2702700,
%T A002548 2882880,360360,110270160,2042040,775975200,162954792,56904848,2586584,
%U A002548 1427794368,892371480,116008292400,120470149800,1124388064800
%N A002548 Denominators of coefficients for numerical differentiation.
%C A002548 Denominator of 1-2HarmonicNumber[n]/(n+1). - Eric Weisstein (eric(AT)weisstein.com), 
               Apr 15, 2004
%C A002548 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
%C A002548 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
%D A002548 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002548 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002548 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).
%D A002548 A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for 
               numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924.
%H A002548 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrianglePointPicking.html">Triangle Point Picking</a>
%H A002548 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SimplexSimplexPicking.html">Simplex Simplex Picking</a>
%F A002548 G.f.: (-ln(1-x))^2 (for fractions A002547(n)/A002548(n))
%F A002548 A002547(n)/A002548(n)=2 stirling1(n+2, n)(-1)^n/(n+2)!
%e A002548 0, 0, 1/12, 1/6, 43/180, 3/10, 197/560, 499/1260, 5471/12600, ...
%p A002548 with(combinat): seq(denom(stirling1(j+2,2)/(j+2)!*2!*(-1)^j),j=0..50);
%Y A002548 Cf. A002547, A093762.
%Y A002548 Sequence in context: A119870 A038332 A093763 this_sequence A038598 A038333 
               A090438
%Y A002548 Adjacent sequences: A002545 A002546 A002547 this_sequence A002549 A002550 
               A002551
%K A002548 nonn,frac
%O A002548 2,3
%A A002548 N. J. A. Sloane (njas(AT)research.att.com).
%E A002548 More terms, GF, formula, Maple code from Barbara Margolius (b.margolius(AT)math.csuohio.edu), 
               Jan 19, 2002
%E A002548 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion 
               of Andrew Plewe, Jun 16 2007

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