This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002428 M2131 N0844 #45 Feb 27 2022 15:51:57
%S A002428 0,1,-2,23,-44,563,-3254,88069,-11384,1593269,-15518938,31730711,
%T A002428 -186088972,3788707301,-5776016314,340028535787,-667903294192,
%U A002428 10823198495797,-5476065119726,409741429887649,-103505656241356,17141894231615609
%N A002428 Numerators of coefficients of expansion of arctan(x)^2 = x^2 - 2/3*x^4 + 23/45*x^6 - 44/105*x^8 + 563/1575*x^10 - 3254/10395*x^12 + ...
%C A002428 |a(n)| = numerator of Sum_{k=1..n} 1/(n*(2*k-1)).
%C A002428 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
%D A002428 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.
%D A002428 H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 313.
%D A002428 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002428 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002428 G. C. Greubel, <a href="/A002428/b002428.txt">Table of n, a(n) for n = 1..1000</a>
%F A002428 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
%t A002428 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 *)
%t A002428 a[n_]:= SeriesCoefficient[ArcTan[x]^2, {x, 0, 2*n-2}]//Numerator; Table[a[n], {n, 1, 30}] (* _G. C. Greubel_, Jul 03 2019 *)
%o A002428 (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 */
%o A002428 (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
%o A002428 (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
%o A002428 (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
%Y A002428 Cf. A071968.
%Y A002428 Cf. A002549, A004041, A025550, A035048.
%K A002428 sign,easy,frac
%O A002428 1,3
%A A002428 _N. J. A. Sloane_
%E A002428 More terms from _Jason Earls_, Apr 09 2002
%E A002428 Additional comments from _Benoit Cloitre_, Apr 06 2002