This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002547 Numerator of {n-th harmonic number H(n) divided by (n+1)}: a(n) = A001008(n)/A002805(n). (Formerly M4765 N2036) 4
 1, 1, 11, 5, 137, 7, 363, 761, 7129, 671, 83711, 6617, 1145993, 1171733, 1195757, 143327, 42142223, 751279, 275295799, 55835135, 18858053, 830139, 444316699, 269564591, 34052522467, 34395742267, 312536252003, 10876020307, 9227046511387, 300151059037 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numerators of coefficients for numerical differentiation. Numerator of u(n)=sum( k=1, n-1, 1/(k(n-k)) ) (u(n) is asymptotic to 2*log(n)/n). - Benoit Cloitre, Apr 12 2003; corrected by Istvan Mezo, Oct 29 2012 a(n) is also the numerator of 2*int(x^(n+1)*log(x/(1-x)),x=0..1). - Groux Roland, May 18 2011 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 Alois P. Heinz, Table of n, a(n) for n = 1..700 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] Eric Weisstein's World of Mathematics, Harmonic Number FORMULA G.f.: (-log(1-x))^2 (for fractions A002547(n)/A002548(n)). - Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002 A002547(n)/A002548(n) = 2*Stirling_1(n+2, 2)(-1)^n/(n+2)! - Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002 EXAMPLE H(n) = Sum[1/i,{i,1,n}] begins 1, 3/2, 11/6, 25/12, ... so H(n)/(n+1) begins 1/2, 1/2, 11/24, 5/12, ... so a(4) = 5. MAPLE with(combinat):seq(numer(stirling1(j+1, 2)/(j+1)!*2!*(-1)^(j+1)), j=1..50); # Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002 MATHEMATICA Numerator[HarmonicNumber[n]/(n+1)] CROSSREFS Cf. A002548, A001008, A002805. Sequence in context: A229525 A174103 A038319 * A090840 A227775 A204011 Adjacent sequences:  A002544 A002545 A002546 * A002548 A002549 A002550 KEYWORD nonn,frac AUTHOR EXTENSIONS More terms from Barbara Margolius (b.margolius(AT)math.csuohio.edu), Jan 19 2002 Simpler definition from Alexander Adamchuk, Oct 31 2004 Offset corrected by Gary Detlefs, Sep 08 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.