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A256195 Number of permutations in S_n that avoid the pattern 25314.

%I A256195 #31 Sep 29 2021 02:34:39
%S A256195 1,1,2,6,24,119,694,4578,33184,258757,2136978,18478134,165857600,
%T A256195 1535336290,14584260700,141603589300,1400942032152,14087464765300,
%U A256195 143689133196008,1484090443264936,15499968503875136,163501005435759505,1740170514634463426,18671118911254798454
%N A256195 Number of permutations in S_n that avoid the pattern 25314.
%H A256195 Anthony Guttmann, <a href="/A256195/b256195.txt">Table of n, a(n) for n = 0..26</a>
%H A256195 Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, <a href="https://arxiv.org/abs/2109.13485">Classical length-5 pattern-avoiding permutations</a>, arXiv:2109.13485 [math.CO], 2021.
%H A256195 Zvezdelina Stankova-Frenkel and Julian West, <a href="http://arxiv.org/abs/math/0103152">A new class of Wilf-equivalent permutations</a>, arXiv:math/0103152 [math.CO], 2001.
%t A256195 avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
%t A256195     lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
%t A256195     psn = Permutations[Range[n]]},
%t A256195    For[i = 1, i <= Length[lpat], i++,
%t A256195     p = lpat[[i]];
%t A256195     AppendTo[lseq, Select[psn, MemberQ[#, {___, p[[p1]], ___, p[[p2]], ___, p[[p3]], ___, p[[p4]], ___, p[[p5]], ___}, {0}] &]];
%t A256195     ]; n! - Length[Union[Flatten[lseq, 1]]]];
%t A256195 Table[avoid[n, {2, 5, 3, 1, 4}], {n, 0, 8}]  (* _Robert Price_, Mar 27 2020 *)
%Y A256195 Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
%Y A256195 Cf. A099952.
%K A256195 nonn
%O A256195 0,3
%A A256195 _N. J. A. Sloane_, Mar 19 2015
%E A256195 a(14)-a(16) from _Bert Dobbelaere_, Mar 18 2021
%E A256195 More terms from _Anthony Guttmann_, Sep 29 2021