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%I #29 Jul 06 2021 16:58:17
%S 0,0,1,1,8,37,248,1749,14284,130343,1318194,14630853,176881314,
%T 2313878809,32567413038,490762544907,7883735348152,134496767915753,
%U 2428518101193448,46270707955530689,927734890186657436
%N Number of permutations of [n] with both a fixed point and a succession.
%C A succession of a permutation p is the appearance of [k,k+1], e.g. in 23541, 23 is a succession.
%e a(4) = 8 because we have 1234, 1243, 1342, 1423, 2134, 2314, 3124 and 4231.
%o (PARI) A201452(n)=my(p,c);sum(k=1,n!,p=numtoperm(n,k);c=(p[1]==1);for(j=2,n,p[j]==j&c!=1&c++==3&break;p[j]-1==p[j-1]&c!=2&(c+=2)==3&break);c==3) \\ - _M. F. Hasler_, Jan 13 2013
%Y Cf. A002467, A180191, A207819, A207821.
%K nonn,more
%O 0,5
%A _Jon Perry_, Jan 09 2013
%E Values a(1..10) double-checked by _M. F. Hasler_, Jan 13 2013
%E a(11)-a(13) from _Alois P. Heinz_, Jan 18 2013
%E a(14)-a(20) from _Alois P. Heinz_, Jul 06 2021
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