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%I A002545 M2651 N1058 #42 Nov 17 2018 20:45:11
%S A002545 1,3,7,15,29,469,29531,1303,16103,190553,128977,9061,30946717,
%T A002545 39646461,58433327,344499373,784809203,169704792667,665690574539,
%U A002545 5667696059,337284946763,7964656853269,46951444927823,284451446729,1597747168263479,816088653136373
%N A002545 Numerator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
%C A002545 Numerators of coefficients for numerical differentiation.
%C A002545 a(n)/A002546(n) = 3*int(x^(n-1)*log^2(x/(1-x)),x=0..1)-(Pi^2)/n. - _Groux Roland_, Nov 13 2009
%C A002545 For prime p >= 5, a(p) == -2*Bernoulli(p-3) (mod p). (See Zhao link.) - _Michel Marcus_, Feb 05 2016
%D A002545 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 A002545 A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924.
%D A002545 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002545 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002545 W. G. Bickley and J. C. P. Miller, <a href="/A002551/a002551.pdf">Numerical differentiation near the limits of a difference table</a>, Phil. Mag., 33 (1942), 1-12 (plus tables) [Annotated scanned copy]
%H A002545 A. N. Lowan, H. E. Salzer and A. Hillman, <a href="/A002545/a002545.pdf">A table of coefficients for numerical differentiation</a>, Bull. Amer. Math. Soc., 48 (1942), 920-924. [Annotated scanned copy]
%H A002545 Jianqiang Zhao, <a href="http://dx.doi.org/10.1016/j.jnt.2006.05.005">Bernoulli numbers, Wolstenholme's theorem, and p^5 variations of Lucas' theorem</a>, Journal of Number Theory, Volume 123, Issue 1, March 2007, Pages 18-26. See Corollary 4.2 p. 25.
%F A002545 G.f.: (-log(1-x))^3 (for fractions A002545(n)/A002546(n)). - Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002
%F A002545 A002545(n)/A002546(n) = 6*Stirling_1(n+3, 3)*(-1)^n/(n+3)!. - Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002
%p A002545 seq(numer(-Stirling1(j, 3)/j!*3!*(-1)^j), j=3..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002
%t A002545 Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}] (* _Ryan Propper_ *)
%Y A002545 Cf. A002546.
%K A002545 nonn,frac
%O A002545 3,2
%A A002545 _N. J. A. Sloane_
%E A002545 More terms from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

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