How to find the general term of this recursive sequence?

Asked May 19 '19 at 18:00

Active May 19 '19 at 18:11

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$$ (a_n)_{a \ge 1}, a_{n+1} = (n+1)a_n + 1, a_1 = 1 $$

I found the first 5 terms and I got 1, 3, 10, 41, 206, but I don't know what to do next? I tries OEIS but it just shows me the recursive formula again. I know that the answer is $ a_n = n!(1 + 1/2! + ... + 1/n!) $ but how do I get to that?

asked May 19 '19 at 18:00

i_suck_at_math

5

Possible duplicate of Solve recurrence relation $ a_{n+1} = (n+1)a_n + 1$ - initial condition there $a_0=1$ instead of $a_1=1$, but that is just a detail – Sil May 19 '19 at 18:03
You can prove this by induction. – May 19 '19 at 18:04

How to find the general term of this recursive sequence?

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