SF34 HAS CLOSE ENCOUNTER WITH A SKYDIVING JUMP PLANE ON DEP FROM EAU.

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THE EVENT OCCURRED BECAUSE ATC TOLD US TO TURN N INTO THE DSNDING TFC INSTEAD OF S. THE JUMP ZONE IS N OF THE COURSE FROM EAU TO ZZZ AND I HAVE NEVER HAD A PROB WITH THE ZONE BEFORE. A CONTRIBUTING FACTOR IS THE EXCESSIVE DSCNT THAT THE JUMP PLANE WAS MAKING IN ORDER TO BEAT THE JUMPERS TO THE GND. FLT X DEPARTED RWY 22 AT EAU AND MADE A L TURN OUT ON COURSE TO ZZZ CLBING OUT OF 5000 FT MSP CTR (125.3) TOLD US TO EXPEDITE OUR CLB THROUGH 7000 FT FOR A JUMP PLANE THAT WAS DSNDING N OF US. THEN ATC TOLD US TO TURN 20 DEGS L FOR TFC. WE COMPLIED WITH ATC AND SOON WE COULD SEE THE ACFT ON TCAS DSNDING RAPIDLY. WE GOT TCAS TA AND NOW TURNED 20 DEGS MORE L (N) TO AVOID THE TFC. WE ADVISED ATC THAT WE WERE DEVIATING AND CTLR STATED THAT OUR RADAR TARGETS WERE GOING TO MERGE. WE WERE STILL CLBING TO 9000 FT; OUR ASSIGNED ALT; WHEN WE GOT A TCAS RA (MONITOR VERT RATE). WE THEN SAW THE JUMP PLANE IN A STEEP TURNING DIVE OBLIVIOUS TO ANY TFC. WE TURNED FURTHER N TO AVOID HIM AND THEN WE GOT ANOTHER TCAS RA TO CLB BECAUSE HE DSNDED THROUGH OUR ALT. I COMPLIED WITH THE RA AGAIN AND WE ADVISED ATC THAT WE HAD MULTIPLE TCAS RA'S. AFTER WE GOT THE CLR OF CONFLICT FROM THE TCAS WE CONTINUED ON COURSE TO ZZZ AND LANDED UNEVENTFULLY. WE COMPLIED WITH THE TCAS RA'S. I THINK THE ATC CTLR SHOULD HAVE TURNED US S INSTEAD OF N. THIS WOULD HAVE AVOIDED THE TFC CONFLICT. ALSO THE JUMP ACFT NEEDS TO CLR THE AREA AND ASK ATC IF ANY TFC IS IN THE AREA BEFORE STARTING SUCH STEEP DSCNTS. THE ACFT WAS IN CONTACT WITH ATC AND TOLD HER THE JUMPERS WERE AWAY; YET HE MADE NO EFFORT TO ARREST HIS DSCNT OR MAKE ANY TURNS TO AVOID US.