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 A370766 #9 Mar 06 2024 17:57:42
%S A370766 1,2,4,20,156,1540,18268,253380,4024220,72006788,1433150940,
%T A370766 31402068292,751081569820,19471227247620,543821277818972,
%U A370766 16278774958879940,519912803924769948,17646698226141369220,634307673944308523740,24070514898945667594308
%N A370766 Number of signed permutations of length n with adjacent elements differing by more than 1.
%C A370766 A signed permutation is a sequence (x_1,x_2,...,x_n) of integers such that {|x_1|,|x_2|,...|x_n|} = {1,2...,n}.
%C A370766 Adjacent elements that differ in sign will always differ by more than 1.
%H A370766 Andrew Howroyd, <a href="/A370766/b370766.txt">Table of n, a(n) for n = 0..200</a>
%F A370766 a(n) = A370767(n) + A370767(n-1) for n > 0.
%F A370766 a(n) = (1+2*n)*a(n-1) + (1-2*n)*a(n-2) + (9-2*n)*a(n-3) + (-6+2*n)*a(n-4) for n >= 4.
%e A370766 In the following examples, the number of assignments of signs to each unsigned permutation is shown in parenthesis.
%e A370766 a(2) = 4: 12(2), 21(2). Total is 2 + 2 = 4.
%e A370766 a(3) = 20: 123(2), 132(4), 213(4), 231(4), 312(4), 321(2).
%o A370766 (PARI) a(n)=subst(serlaplace(polcoef((1 + x)/(1 + (1 - 2*y)*x + 2*y*x^2) + O(x*x^n), n)), y, 1)
%Y A370766 Cf. A370767, A370768.
%K A370766 nonn
%O A370766 0,2
%A A370766 _Andrew Howroyd_, Mar 01 2024