How to prove reduction of this induction to formula?

Revision en2, by prudent, 2019-06-16 10:40:58

$$$a_1 = 1$$$
$$$a_2 = 5$$$
$$$a_n = a_{n-1} + n^2(a_{n-2}+1)$$$

Prove $$$a_n=(n+1)!-1$$$
P.S. Original problem

Tags #induction, #reduction, #formula, #dp

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en3 English prudent 2019-06-16 11:32:59 9
en2 English prudent 2019-06-16 10:40:58 99
en1 English prudent 2019-06-16 10:33:13 138 Initial revision (published)