cp's OEIS Frontend

A193777 Number of signed permutations of size 2n invariant under D and D'bar and avoiding (-2, 1) and (2, -1).

%I A193777 #30 Jun 26 2019 07:52:31
%S A193777 1,2,6,18,58,190,642,2206,7746,27662,100738,373550,1413506,5457710,
%T A193777 21546466,87025806,360264258,1529624366,6669850466,29877013902,
%U A193777 137560725890,650780790894,3162711095074,15774862353614,80687636530882,422713072650286,2265833731786594
%N A193777 Number of signed permutations of size 2n invariant under D and D'bar and avoiding (-2, 1) and (2, -1).
%C A193777 Also the number of signed permutations of size n invariant under D and avoiding (-2, 1) and (2, -1).
%H A193777 Andy Hardt and Justin M. Troyka, <a href="https://people.carleton.edu/~eegge/rssp.pdf">Restricted Symmetric Signed Permutations</a>, 2012.
%F A193777 a(n) = 2*a(n-1) + n*a(n-2) - Sum_{j=1..k-3} j*a(j)*|S_{k-j-3}^D|, where S_n^D is the set of unsigned permutations of length n invariant under D.
%F A193777 a(n) = 2*a(n-1) + n*a(n-2) - Sum_{j=1..n-3} j*a(j)*A000085(n-j-2). - _Andrew Howroyd_, Dec 09 2018
%p A193777 inv := proc(n) option remember; if n<2 then 1 else inv(n-1)+(n-1)*inv(n-2) fi end:
%p A193777 a := proc(n) option remember; if n < 2 then n+1 else
%p A193777 2*a(n-1) + n*a(n-2) - add(j*a(j)*inv(n-j-2), j=1..n-3) fi end:
%p A193777 seq(a(n), n=0..26); # _Peter Luschny_, Dec 09 2018
%t A193777 inv[n_] := inv[n] = If[n<2, 1, inv[n-1] + (n-1) inv[n-2]];
%t A193777 a[n_] := a[n] = If[n<2, n+1, 2 a[n-1] + n a[n-2] - Sum[j a[j] inv[n-j-2], {j, 1, n-3}]];
%t A193777 Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Jun 26 2019, after _Peter Luschny_ *)
%Y A193777 Cf. A193778, A000085.
%K A193777 nonn
%O A193777 0,2
%A A193777 _Andy Hardt_, Aug 04 2011
%E A193777 Terms a(9) and beyond from _Peter Luschny_, Dec 09 2018