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 A005983 M5347 #29 Jul 08 2025 16:40:36
%S A005983 1,1,70,26599,33757360,107709888805,726401013530416,
%T A005983 9197888739246870571,200656681438694771057920,
%U A005983 7065183006232334215872360169,381446884048286939903298793116160,30299510478473850351087119774475282895,3422529682416045761005260546463028151218176
%N A005983 Number of 4 up, 4 down, 4 up, ... permutations of length 4n+1.
%D A005983 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A005983 P. R. Stein, personal communication.
%H A005983 Alois P. Heinz, <a href="/A005983/b005983.txt">Table of n, a(n) for n = 0..132</a>
%H A005983 P. R. Stein and N. J. A. Sloane, <a href="/A005981/a005981.pdf">Correspondence, 1975</a>
%p A005983 b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=4,
%p A005983 b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
%p A005983 end:
%p A005983 a:= n-> b(0, 4*n+1, 0):
%p A005983 seq(a(n), n=0..20); # _Alois P. Heinz_, Oct 06 2013
%t A005983 b[u_, o_, t_] := b[u, o, t] = If[u+o == 0, 1, Sum[If[t == 4, b[o-j, u+j-1, 1], b[u+j-1, o-j, t+1]], {j, 1, o}]] ; a[n_] := b[0, 4*n+1, 0]; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Nov 25 2014, after _Alois P. Heinz_ *)
%Y A005983 Cf. A229885.
%K A005983 nonn
%O A005983 0,3
%A A005983 _N. J. A. Sloane_
%E A005983 Typo in name fixed by _Alois P. Heinz_, Oct 06 2013