a(n) are the primes from A091415[n] = {2,3,4,8,13,32,41,45,59,97,107,364,421,...} Numbers n such that n!*2^n - 1 is prime. Corresponding primes of the form (2p)!! - 1 are {3,5,270269,26226140915375977206881249, 58431212742946338570036120182498518593749,...}