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A264460 Number of permutations of [n] with exactly one occurrence of the generalized pattern 23-1.

%I A264460 #14 Sep 28 2020 07:53:38
%S A264460 1,6,32,171,944,5444,32919,208816,1388240,9657929,70187054,531857288,
%T A264460 4194927585,34379859346,292303350268,2574284790795,23450837821836,
%U A264460 220681535036288,2142618638738279,21438586249394500,220827871704427308,2339281577294955745
%N A264460 Number of permutations of [n] with exactly one occurrence of the generalized pattern 23-1.
%H A264460 Alois P. Heinz, <a href="/A264460/b264460.txt">Table of n, a(n) for n = 3..500</a>
%e A264460 a(3) = 1: 231.
%e A264460 a(4) = 6: 1342, 2314, 2413, 2431, 3241, 4231.
%p A264460 b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
%p A264460       b(u-j, o+j-1), j=1..u) +add(convert(series(
%p A264460       b(u+j-1, o-j)*x^u, x, 2), polynom), j=1..o))
%p A264460     end:
%p A264460 a:= n-> coeff(b(n, 0), x, 1):
%p A264460 seq(a(n), n=3..25);
%t A264460 b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[u-j, o+j-1], {j, 1, u}] + Sum[Series[b[u+j-1, o-j] x^u, {x, 0, 2}] // Normal, {j, 1, o}]];
%t A264460 a[n_] := Coefficient[b[n, 0], x, 1];
%t A264460 a /@ Range[3, 25] (* _Jean-François Alcover_, Sep 28 2020, after Maple *)
%Y A264460 Column k=1 of A260670.
%K A264460 nonn
%O A264460 3,2
%A A264460 _Alois P. Heinz_, Nov 14 2015