%I #14 Jul 24 2017 11:57:31
%S 7,41,176075177,49127973630377
%N Primes in A290044.
%C For n < 20, A290044(n) are prime when n = {2, 3, 9, 13}.
%C For n >= 20, 19|A290044(n). Therefore there are only 4 terms in this sequence.
%e 41 = |0!! - 2!! + 4!! - 6!!| is prime.
%t Select[Table[Abs@ Sum[(-1)^k*(2 k)!!, {k, 0, n}], {n, 0, 60}], PrimeQ] (* _Michael De Vlieger_, Jul 19 2017 *)
%Y Cf. A006882, A071828, A290044.
%K nonn,fini,full
%O 1,1
%A _XU Pingya_, Jul 19 2017