The 5th power of the g.f. equals the g.f. of A196344.

Terms

a(0) =1a(1) =1a(2) =-2a(3) =6a(4) =-21a(5) =80a(6) =-320a(7) =1326a(8) =-5637a(9) =24434a(10) =-107542a(11) =479196a(12) =-2157045a(13) =9792702a(14) =-44780606a(15) =206055345a(16) =-953305628a(17) =4431463845a(18) =-20686696836a(19) =96931500441a(20) =-455722376856