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 A106181 #12 Jul 29 2021 07:26:26 %S A106181 0,1,-1,-1,2,2,-5,-5,14,14,-42,-42,132,132,-429,-429,1430,1430,-4862, %T A106181 -4862,16796,16796,-58786,-58786,208012,208012,-742900,-742900, %U A106181 2674440,2674440,-9694845,-9694845,35357670,35357670,-129644790,-129644790,477638700,477638700,-1767263190,-1767263190 %N A106181 Expansion of c(-x^2)(1+2x-sqrt(1+4x^2))/2, c(x) the g.f. of A000108. %C A106181 Second column of number triangle A106180. %F A106181 a(n) = sin(Pi*n/2)*(C((n-1)/2)*(1-(-1)^n)/2) + sin(Pi*(n+1)/2)*(C(n/2)*(1+(-1)^n)/2) - 0^n for n > 0. %F A106181 Conjecture: (n+2)*a(n) + n*a(n-1) + 4*(n-1)*a(n-2) + 4*(n-3)*a(n-3) = 0. - _R. J. Mathar_, Nov 15 2011 %Y A106181 Cf. A000108, A099363. %K A106181 easy,sign %O A106181 0,5 %A A106181 _Paul Barry_, Apr 24 2005