%I M1110 N0424 #29 Nov 17 2018 21:31:11

%S 1,2,4,8,15,240,15120,672,8400,100800,69300,4950,17199000,22422400,

%T 33633600,201801600,467812800,102918816000,410646075840,3555377280,

%U 215100325440,5162407810560,30920671782000,190281057120,1085315579548200,562756226432400,22969641895200

%N Denominator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).

%C Denominators of coefficients for numerical differentiation.

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

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

%H 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 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]

%F 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(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 seq(denom(-Stirling1(j, 3)/j!*3!*(-1)^j), j=3..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002

%t Denominator[Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}]] (* _Ryan Propper_ *)

%Y Cf. A002545.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_

%E More terms from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002