It's all about the Bonus Points

Bn=nBn1+1\large B_n = n B_{n-1} + 1

Let BnB_n satisfy the recurrence relation above for B=1,2,3,B=1,2,3,\ldots and B0=1B_0 = 1. What is B10B_{10} ?

Bonus:

  • You can show me how do derive a closed form solution to this recursion sequence. It exists but I do not know how to derive it yet.

  • You can interpret this question intuitively and give a real world example of when such a sequence would occur/count.

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