A085507 Stirling transform of the prime characteristic function.

0, 0, 1, 4, 13, 41, 136, 505, 2171, 10693, 58246, 340242, 2095435, 13492077, 90267633, 623383765, 4414350135, 31899350954, 235002008725, 1773013299342, 13855253098226, 114135759054965, 1010686200326760, 9744658443894282