k[1] = 1/50
k[2] = 1096119423/2000000000
k[3] = 944338309/500000000
k[4] = 746728086949361/10000000000000
k[5] = 106090440772217/1000000000000
k[6] = 249828053/125000000
k[7] = 1224372434018557141566569050370849451/1205573190593375000000000000000000000
k[8] = 12241102221402998526331/232012016212744100000000
k[9] = 98652827/156250000
k[10] = 1058581849/100000000
k[11] = 8104001078261174959272626909130835101/96445855247470000000000000000000000
k[12] = 1949540411/10000000000
k[13] = 8050459589/10000000000
k[14] = 1832090242206401314030413/5800300405318602500000000
k[15] = 2337873603/2500000000
k[16] = 783656669828271/1000000000000000
k[17] = 838679653/5000000000
k[18] = 19205783238971/125000000000000
k[19] = 38411411216101/2500000000000
k[20] = 67601459488567/25000000000000
k[21] = 1