k[1] = 1/5
k[2] = 420467092599869/500000000000000
k[3] = 55069267386123/25000000000000
k[4] = 1527008609158553/20000000000000
k[5] = 120
k[6] = 7994497695001/4000000000000
k[7] = 244890375207854787969804290882092215119191/192000000000000000000000000000000000000000
k[8] = 137553007555861/1000000000000000
k[9] = 101961166850901/125000000000000
k[10] = 304586590049657/50000000000000
k[11] = 242908532752465070558567520972847500687/4000000000000000000000000000000000000
k[12] = 172622515189057/1000000000000000
k[13] = 827377484810943/1000000000000000
k[14] = 46757657636931/1000000000000000
k[15] = 46757657636931/500000000000000
k[16] = 15709821429/10000000000
k[17] = 189811268010923/5000000000000000
k[18] = 15709821429/10000000000
k[19] = 15709821429/10000000000
k[20] = 15709821429/10000000000
k[21] = 1