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A275825 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.

%I A275825 #41 Jul 22 2025 18:39:30
%S A275825 1,1,1,2,5,14,52,238,1288,8144,59150,486080,4464304,45352840,
%T A275825 505200280,6124903616,80304039608,1132339758992,17089219746352,
%U A275825 274872988654576,4694355262548640,84840179120802560,1617735736056994736,32457990536915964800,683569125395013719680
%N A275825 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 A275825 Robert Israel, <a href="/A275825/b275825.txt">Table of n, a(n) for n = 0..450</a>
%F A275825 a(n) ~ c * n^(n-5/2) / exp(n), where c = 35.33624296996624315241349866820530476... . - _Vaclav Kotesovec_, Oct 04 2016
%p A275825 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 A275825 map(f, [$0..30]); # _Robert Israel_, Nov 08 2016
%t A275825 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}]
%t A275825 nxt[{n_,a_,b_,c_}]:={n+1,b,c,c(n-2)+n*a}; NestList[nxt,{2,1,1,1},30][[;;,2]] (* _Harvey P. Dale_, Jul 22 2025 *)
%o A275825 (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 A275825 Cf. A000930, A000931.
%K A275825 nonn
%O A275825 0,4
%A A275825 _Christopher C. Capobianco_, Sep 13 2016