This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A130309 #9 Jul 18 2019 14:29:16
%S A130309 2,3,7,67,153979499670311863,
%T A130309 96139392052480758114443739387402080695373863
%N A130309 Primes of the form [k!! - (k-1)!! + (k-2)!! -....1!!] + 1.
%C A130309 The next term is too large to include.
%C A130309 The corresponding values of k are 1, 2, 3, 4, 7, 31, 63, 263, 311, 371, 383, 10243, ... (1 and 2 give the same prime, 2). All these values except 2 and 4 are odd since for k even above 10 this form is divisible by 7. a(11) ~ 2.060 * 10^18317. - _Amiram Eldar_, Jul 18 2019
%H A130309 Amiram Eldar, <a href="/A130309/b130309.txt">Table of n, a(n) for n = 1..10</a>
%e A130309 2 = 1!! + 1 or 2!! - 1!! + 1.
%e A130309 7 = 4!! - 3!! + 2!! - 1!! +1 = 8 - 3 + 2 - 1 + 1.
%p A130309 P:=proc(n) local a,i,j,k,w; for i from 1 by 1 to n do a:=0; for j from i by -1 to 0 do k:=j; w:=j-2; while w>0 do k:=k*w; w:=w-2; od; a:=a+k*(-1)^j od; if isprime(abs(a)+1) then print(abs(a)+1); fi; od; end: P(1000);
%t A130309 f[n_] := Sum[(-1)^(n-k)*k!!, {k, 1, n}] + 1; Select[f/@Range[2, 31], PrimeQ] (* _Amiram Eldar_, Jul 18 2019 *)
%Y A130309 Cf. A071828, A130308.
%K A130309 nonn
%O A130309 1,1
%A A130309 _Paolo P. Lava_ and _Giorgio Balzarotti_, May 21 2007