OFFSET
3,2
COMMENTS
Numerators of coefficients for numerical differentiation.
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
For prime p >= 5, a(p) == -2*Bernoulli(p-3) (mod p). (See Zhao link.) - Michel Marcus, Feb 05 2016
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).
LINKS
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) [Annotated scanned copy]
A. N. Lowan, H. E. Salzer and A. Hillman, A table of coefficients for numerical differentiation, Bull. Amer. Math. Soc., 48 (1942), 920-924. [Annotated scanned copy]
Jianqiang Zhao, Bernoulli numbers, Wolstenholme's theorem, and p^5 variations of Lucas' theorem, Journal of Number Theory, Volume 123, Issue 1, March 2007, Pages 18-26. See Corollary 4.2 p. 25.
FORMULA
MAPLE
seq(numer(-Stirling1(j, 3)/j!*3!*(-1)^j), j=3..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002
MATHEMATICA
Table[Sum[1/i/j/(n-i-j), {i, n-2}, {j, n-i-1}], {n, 3, 100}] (* Ryan Propper *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
More terms from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002
STATUS
approved