a(n) = B(n) - 1, where B(n) = Bell numbers, A000110.

Terms

a(0) =1a(1) =4a(2) =14a(3) =51a(4) =202a(5) =876a(6) =4139a(7) =21146a(8) =115974a(9) =678569a(10) =4213596a(11) =27644436a(12) =190899321a(13) =1382958544a(14) =10480142146a(15) =82864869803a(16) =682076806158