MathDB

Let

T_0=2, T_1=3, T_2=6,

and for

n\ge 3

T_n=(n+4)T_{n-1}-4nT_{n-2}+(4n-8)T_{n-3}.

The first few terms are

2, 3, 6, 14, 40, 152, 784, 5158, 40576, 363392.

Find a formula for

T_n

of the form

T_n=A_n+B_n,

where

\{A_n\}

and

\{B_n\}

are well known sequences.

A1