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Third-order sequence with non-constant coefficients: a(n) = (n-3)*a(n-1) + (n-1)*a(n-3); a(0) = a(1) = a(2) = 1.
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%I #39 Nov 08 2016 22:20:11

%S 1,1,1,2,5,14,52,238,1288,8144,59150,486080,4464304,45352840,

%T 505200280,6124903616,80304039608,1132339758992,17089219746352,

%U 274872988654576,4694355262548640,84840179120802560,1617735736056994736,32457990536915964800,683569125395013719680

%N Third-order sequence with non-constant coefficients: a(n) = (n-3)*a(n-1) + (n-1)*a(n-3); a(0) = a(1) = a(2) = 1.

%H Robert Israel, <a href="/A275825/b275825.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) ~ c * n^(n-5/2) / exp(n), where c = 35.33624296996624315241349866820530476... . - _Vaclav Kotesovec_, Oct 04 2016

%p f:= gfun:-rectoproc({a(n) = (n-3)*a(n-1) + (n-1)*a(n-3), a(0) = 1,a(1) = 1, a(2) = 1}, a(n), remember):

%p map(f, [$0..30]); # _Robert Israel_, Nov 08 2016

%t RecurrenceTable[{a[n+1]==(n-2)*a[n]+n*a[n-2],a[0]==1,a[1]==1,a[2]==1},a,{n,0,15}]

%o (C) int seq(int n) {int v = 1; if(n <= 2) {v = 1;} else {v = (n-3)*seq(n-1) + (n-1)*seq(n-3);}return v;}

%Y Cf. A000930, A000931.

%K nonn

%O 0,4

%A _Christopher C. Capobianco_, Sep 13 2016