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 A191798 #12 Mar 30 2017 23:35:50 %S A191798 0,2,58,2474,180480,19895936,3105348340,652948189204,177662757810868, %T A191798 60772232945639507,25533219938917963508,12921764841857675170314, %U A191798 7754002391777621430686566 %N A191798 Number of essentially different ways of arranging numbers 1 through 2*n around a circle so that the sums of each pair of adjacent numbers are neither all prime nor all composite. %C A191798 Finding a pattern, recurrence relation or explicit formula for this sequence would allow us to find terms in A191374 using terms from A051252, or vice versa. %F A191798 For n>1, a(n) = (2*n-1)!/2 - A051252(n) - A191374(n). %e A191798 a(2) = 2 since the arrangements 1,3,2,4 and 1,3,4,2 both satisfy the condition. %Y A191798 Cf. A051252, A191374. %K A191798 nonn,more %O A191798 1,2 %A A191798 _Bennett Gardiner_, Jun 16 2011 %E A191798 a(7) corrected, a(8)-a(13) added by _Max Alekseyev_, Aug 19 2013