%I #12 Jun 08 2021 02:33:32
%S 0,0,1,2,7,14,47,104,383,944,3839,10394,46079,135134,645119,2027024,
%T 10321919,34459424,185794559,654729074,3715891199,13749310574,
%U 81749606399,316234143224,1961990553599,7905853580624,51011754393599
%N a(n) = n!! - 1.
%C n divides a(n-1) and a(n+1) for n = {1, 2, 8, 11, 16, 19, 23, 31, 32, 43, 64, 67, 71, ...} which include all powers of 2 except 2^2 and some odd primes of the form 4k+3 belonging to A002145.
%C p^2 divides a(p-1) for odd prime p = 71.
%C p^2 divides a(p+1) for odd prime p = 23.
%C a(n) is prime for n = {3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, ...} = A007749; A007749(n) = 2*A091415(n-1) for n > 1. Corresponding primes of the form n!! - 1 are listed in A117141, cf. also A093173.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DoubleFactorial.html">Double Factorial</a>
%F a(n) = A006882(n) - 1.
%t Table[ n!! - 1, {n,0,35} ]
%Y Cf. A006882, A002145, A117141, A093173, A007749, A091415.
%K nonn
%O 0,4
%A _Alexander Adamchuk_, Apr 18 2007