cp's OEIS Frontend

A361938 a(0)=1, a(1)=0; a(n) = floor(n/2)*(a(n-1) + a(n-2)).

%I A361938 #36 Apr 08 2023 00:30:31
%S A361938 1,0,1,1,4,10,42,156,792,3792,22920,133560,938880,6434640,51614640,
%T A361938 406344960,3663676800,32560174080,326014657920,3227173488000,
%U A361938 35531881459200,387590549472000,4654346740243200,55461310186867200,721387883125324800,9322190319746304000
%N A361938 a(0)=1, a(1)=0; a(n) = floor(n/2)*(a(n-1) + a(n-2)).
%C A361938 For n <= 1000000, n prime divides a(n) only when n=5 and n composite does not divide a(n) only when n = 9. Is this always so?
%F A361938 a(0)=1, a(1)=0; a(n) = floor(n/2)*(a(n-1) + a(n-2)).
%e A361938 a(0) = 1;
%e A361938 a(1) = 0;
%e A361938 a(2) = floor(2/2)*(a(1) + a(0)) = 1;
%e A361938 a(3) = floor(3/2)*(a(2) + a(1)) = 1;
%e A361938 a(4) = floor(4/2)*(a(3) + a(2)) = 4;
%e A361938 a(5) = floor(5/2)*(a(4) + a(3)) = 10.
%t A361938 a[0] = 1; a[1] = 0; a[n_] := a[n] = Floor[n/2] * (a[n - 1] + a[n - 2]); Array[a, 30, 0] (* _Amiram Eldar_, Apr 05 2023 *)
%o A361938 (Python)
%o A361938 def seqx_it(n):
%o A361938   a0 = 1
%o A361938   a1 = 0
%o A361938   sequence_store = [a0,a1]
%o A361938   for i in range (2,n):
%o A361938     a2 = (i//2) * (a1 + a0)
%o A361938     sequence_store.append(a2)
%o A361938     a0 = a1
%o A361938     a1 = a2
%o A361938   return sequence_store
%Y A361938 Cf. A055596.
%K A361938 nonn
%O A361938 0,5
%A A361938 _Davide Oliveri_, Mar 31 2023