Euler transform is sequence A004016.

Terms

a(0) =6a(1) =-21a(2) =76a(3) =-345a(4) =1734a(5) =-8906a(6) =46662a(7) =-250257a(8) =1365388a(9) =-7538421a(10) =42030150a(11) =-236312690a(12) =1338000774a(13) =-7620721077a(14) =43626920908a(15) =-250869973089