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A281262 Number of permutations of [2n] with exactly n fixed points.

%I A281262 #17 Sep 01 2021 03:58:52
%S A281262 1,0,6,40,630,11088,244860,6362928,190900710,6490575520,246642054516,
%T A281262 10358965584240,476512419579196,23825620968559200,1286583532342313400,
%U A281262 74621844875699059680,4626554382293942780550,305352589231397889910080,21374681246197861368840900
%N A281262 Number of permutations of [2n] with exactly n fixed points.
%H A281262 Alois P. Heinz, <a href="/A281262/b281262.txt">Table of n, a(n) for n = 0..366</a>
%F A281262 a(n) = (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n for n>1, a(n) = 1-n for n<2.
%F A281262 a(n) = binomial(2n,n) * A000166(n).
%F A281262 a(n) = A008290(2n,n) = A098825(2n,n).
%e A281262 a(2) = 6: 1243, 1324, 1432, 2134, 3214, 4231.
%p A281262 a:= proc(n) option remember; `if`(n<2, 1-n,
%p A281262       (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n)
%p A281262     end:
%p A281262 seq(a(n), n=0..20);
%t A281262 a[n_] := Binomial[2n, n] Subfactorial[n];
%t A281262 a /@ Range[0, 20] (* _Jean-François Alcover_, Sep 01 2021 *)
%Y A281262 Cf. A000166, A007318, A008290, A098825.
%K A281262 nonn
%O A281262 0,3
%A A281262 _Alois P. Heinz_, Apr 12 2017