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

1, 0, 1, 1, 4, 10, 42, 156, 792, 3792, 22920, 133560, 938880, 6434640, 51614640, 406344960, 3663676800, 32560174080, 326014657920, 3227173488000, 35531881459200, 387590549472000, 4654346740243200, 55461310186867200, 721387883125324800, 9322190319746304000

Offset: 0

Author

Davide Oliveri, Mar 31 2023

Keywords

• nonn

Comments

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?

Examples

			a(0) = 1;
a(1) = 0;
a(2) = floor(2/2)*(a(1) + a(0)) = 1;
a(3) = floor(3/2)*(a(2) + a(1)) = 1;
a(4) = floor(4/2)*(a(3) + a(2)) = 4;
a(5) = floor(5/2)*(a(4) + a(3)) = 10.
		

Crossrefs

Cf. A055596.

Programs

Mathematica

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 *)

Python

def seqx_it(n):
  a0 = 1
  a1 = 0
  sequence_store = [a0,a1]
  for i in range (2,n):
    a2 = (i//2) * (a1 + a0)
    sequence_store.append(a2)
    a0 = a1
    a1 = a2
  return sequence_store

Formula

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