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 A195186 #18 Nov 29 2017 16:57:06
%S A195186 1,2,6,20,72,290,1198,5452,25176,125874,637926,3448708,18919048,
%T A195186 109412210,642798510,3945170012,24614491704,159328958690,
%U A195186 1048645656646,7122719571700,49185991168968,349097516604738,2518145666958126,18609525157571692,139704193446510616
%N A195186 Number of palindromic double occurrence words of length 2n.
%H A195186 Jonathan Burns and Tilahun Muche, <a href="http://arxiv.org/abs/1105.2926">Counting Irreducible Double Occurrence Words</a>, arXiv preprint arXiv:1105.2926 [math.CO], 2011.
%F A195186 Theorem 3.3 of Burns-Muche gives a recurrence.
%p A195186 A047974 := proc(n) option remember; if n= 1 then 1; elif n=2 then 3; else procname(n-1)+2*(n-1)*procname(n-2) ; end if; end proc:
%p A195186 A195186 := proc(n) if n <= 1 then 1; else A047974(n)-add(procname(n-2*k)*doublefactorial(2*k-1),k=1..floor(n/2)) ; end if; end proc:
%p A195186 seq(A195186(n),n=1..20) ; # _R. J. Mathar_, Sep 12 2011
%t A195186 b[n_] := Sum[Binomial[k, n - k]*(n!/k!), {k, 0, n}];
%t A195186 a[1] = 1; a[n_] := b[n] - Sum[a[n - 2*k]*(2*k - 1)!!, {k, 1, n/2}];
%t A195186 Array[a, 20] (* _Jean-François Alcover_, Nov 29 2017, after _R. J. Mathar_ *)
%K A195186 nonn
%O A195186 1,2
%A A195186 _N. J. A. Sloane_, Sep 10 2011