Next term has a "ten" digit.
Also called factoradix.
With hexadecimal extended to use the whole alphabet, the sequence continues: 17a5726651220, 12092315551220, b6781182251220, 799b90920051220, 4c71069221151220, 2dcaa584234451220, 1a1f264b9386651220, fb2797aa5975551220, 8437c58494852251220, 423g9bad8a4580051220, 1k213c54aa81881151220
10^48 needs a "36" digit. We can say with high probability that 10^64 is the last value that can be written without needing any digits larger than 35 (checked up to 10^1400, where it is vanishingly unlikely).