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A193361 a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-3)*a(n-2) + 1.

%I A193361 #26 Sep 08 2022 08:45:58
%S A193361 0,0,1,2,4,9,22,59,170,525,1716,5917,21362,80533,315516,1281913,
%T A193361 5383622,23330405,104084736,477371217,2246811730,10839493637,
%U A193361 53528916508,270318789249,1394426035918,7341439399397,39413238225512,215607783811041,1200938739448842
%N A193361 a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-3)*a(n-2) + 1.
%H A193361 Vincenzo Librandi, <a href="/A193361/b193361.txt">Table of n, a(n) for n = 0..800</a>
%F A193361 a(0)=a(1)=0, a(2)=1, a(n) = 2*a(n-1)+(n-4)*a(n-2)-(n-4)*a(n-3).
%F A193361 a(n) ~ (sqrt(Pi)+sqrt(2))/2 * n^(n/2-1)*exp(sqrt(n)-n/2-1/4) * (1-17/(24*sqrt(n))). - _Vaclav Kotesovec_, Dec 27 2012
%F A193361 a(n) = A187044(n-2). - _Vaclav Kotesovec_, Feb 14 2014
%t A193361 RecurrenceTable[{a[1]==0,a[2]==0,a[n]==a[n-1]+(n-4) a[n-2]+1},a,{n,30}]
%o A193361 (Magma) [n le 2 select 0 else Self(n-1)+(n-4)*Self(n-2) + 1: n in [1..30]];
%Y A193361 Cf. A185108, A185109, A185308, A185309, A186738, A186739, A213720.
%K A193361 nonn,easy
%O A193361 0,4
%A A193361 _Vincenzo Librandi_, Dec 25 2012