OFFSET
1,3
COMMENTS
|a(n)| = numerator of Sum_{k=1..n} 1/(n*(2*k-1)).
Let f(x) = (1/2)*log((1+sqrt(x))/(1-sqrt(x))) and c(n) = Integral_{x=0..1} f(x)*x^(n-1) dx, then for n>=1, c(n) = |a(n+1)|/A071968(n) and (f(x))^2 = Sum_{n>=1} c(n)*x^n. - Groux Roland, Dec 14 2010
REFERENCES
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 89.
H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 313.
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
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = numerator of (-1)^n * Sum_{k=1..n-1} 1/((n-1)*(2*k-1)), for n>=1. - G. C. Greubel, Jul 03 2019
MATHEMATICA
a[n_]:= (-1)^n*Sum[1/((n-1)*(2*k-1)), {k, 1, n-1}]//Numerator; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Nov 04 2013 *)
a[n_]:= SeriesCoefficient[ArcTan[x]^2, {x, 0, 2*n-2}]//Numerator; Table[a[n], {n, 1, 30}] (* G. C. Greubel, Jul 03 2019 *)
PROG
(PARI) vector(30, n, numerator((-1)^n*sum(k=1, n-1, 1/((n-1)*(2*k-1))))) /* corrected by G. C. Greubel, Jul 03 2019 */
(Magma) [0] cat [Numerator((-1)^n*(&+[1/((n-1)*(2*k-1)): k in [1..n-1]])): n in [2..30]]; // G. C. Greubel, Jul 03 2019
(Sage) [numerator((-1)^n*sum(1/((n-1)*(2*k-1)) for k in (1..n-1))) for n in (1..30)] # G. C. Greubel, Jul 03 2019
(GAP) List([1..30], n-> NumeratorRat( (-1)^n*Sum([1..n-1], k-> 1/((n-1)*(2*k-1))) )) # G. C. Greubel, Jul 03 2019
CROSSREFS
KEYWORD
sign,easy,frac
AUTHOR
EXTENSIONS
More terms from Jason Earls, Apr 09 2002
Additional comments from Benoit Cloitre, Apr 06 2002
STATUS
approved