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%I #17 Mar 23 2026 16:57:05
%S 1,2,5,28,204,2000,24030,344652,5740560,109023264,2326287600,
%T 55117624320,1436196484800,40826537706240,1257537996514800,
%U 41726938979325600,1484001670159008000,56319120817785745920,2271900191107266720000,97080540724816485258240
%N Number of circular parking functions of length n avoiding the pattern 111.
%H Lara Pudwell, <a href="https://faculty.valpo.edu/lpudwell/slides/AMS2025.pdf">Pattern avoidance in cyclic parking functions</a>, 2025.
%H Lara Pudwell, <a href="https://faculty.valpo.edu/lpudwell/papers/circpf.pdf">Pattern Avoidance in Circular Parking Functions</a>, Valparaiso Univ. (2026). See p. 6 (Table 2).
%F If n is odd, a(n) = A036774(n+1)/(n*(n+1)).
%F If n is even, a(n) = (A036774(n+1)+(n+1)!/(n/2+1)!)/(n*(n+1)).
%e For n=4, the a(4)=28 parking functions are 1122, 1123, 1124, 1132, 1133, 1134, 1142, 1143, 1212, 1213, 1214, 1223, 1224, 1232, 1233, 1234, 1242, 1243, 1313, 1314, 1322, 1323, 1324, 1332, 1342, 1422, 1423, 1432.
%Y Cf. A019536, A036774, A121774, A171005, A213937, A393352, A394236, A394237.
%K nonn
%O 1,2
%A _Lara Pudwell_, Mar 13 2026