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 A076743 #9 Jun 24 2014 01:08:32
%S A076743 1,-2,6,-2,-24,24,120,-240,24,-720,2400,-720,5040,-25200,15120,-720,
%T A076743 -40320,282240,-282240,40320,362880,-3386880,5080320,-1451520,40320,
%U A076743 -3628800,43545600,-91445760,43545600,-3628800,39916800,-598752000,1676505600
%N A076743 Nonzero coefficients of the polynomials in the numerator of 1/(1+x^2) and its successive derivatives, starting with the highest power of x.
%C A076743 Denominator of n-th derivative is (1+x^2)^(n+1), whose coefficients are the binomial coefficients, A007318.
%C A076743 The unsigned sequence 1,2,6,2,24,24,120,240,24,720,... is n-th derivative of 1/(1-x^2). For 0<=k<=n, let a(n,k) be the coefficient of x^k in the numerator of the n-th derivative of 1/(1-x^2). If n+k is even, a(n,k)=n!*binomial(n+1,k); if n+k is odd, a(n,k)=0. The nonzero coefficients of the numerators starting with the highest power of x are 1; 2; 6,2; 24,24; ... In fact this is the (n-1)-st derivative of arctanh(x). - Rostislav Kollman (kollman(AT)dynasig.cz), Jan 04 2005
%F A076743 For 0<=k<=n, let a(n, k) be the coefficient of x^k in the numerator of the n-th derivative of 1/(1+x^2). If n+k is even, a(n, k) = (-1)^((n+k)/2)*n!*binomial(n+1, k); if n+k is odd, a(n, k)=0.
%e A076743 The nonzero coefficients of the numerators starting with the highest power of x are: 1; -2; 6,-2; -24,24; ...
%t A076743 a[n_, k_] := Coefficient[Expand[Together[(1+x^2)^(n+1)*D[1/(1+x^2), {x, n}]]], x, k]; Select[Flatten[Table[a[n, k], {n, 0, 10}, {k, n, 0, -1}]], #!=0&]
%Y A076743 Cf. A076256, A076257, A076741.
%K A076743 sign,tabf,easy
%O A076743 0,2
%A A076743 _Mohammad K. Azarian_, Nov 11 2002
%E A076743 Edited by _Dean Hickerson_, Nov 28 2002