WI: Andrew Jackson dies early?

Andrew Jackson came close to dying many times OTL prior to becoming president. Not just from the multiple battles, but also from several periods of serious illness and other issues. Suppose that one of those periods of illness is just a bit worse, and he dies much earlier than IOTL, perhaps about 1781 when he apparently contracted smallpox (according to Wikipedia). What happens if he is removed from the scene so early? I can't imagine that the broad sweep of things is much different for some time, but surely by the 1820s there will be some significant differences?
 
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