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I want to get the recurrence relation for several values of n in a grid form. At the moment I am using

RecurrenceTable[{a[n + 2] == (1 - n)/(n + 1) a[n], a[2] == a0, a[3] == 0}, a, {n, 2, 20}]

To get

{a0, 0, -(a0/3), 0, a0/5, 0, -(a0/7), 0, a0/9, 0, -(a0/11), 0, a0/13, 0, -(a0/15), 
 0, a0/17, 0, -(a0/19)}

But I need it with the values of $n$ in one column running from 2 to 20 with heading n and the above list as a second column with heading a[n]. I tried something funny but it failed horribly:

Grid[Table[{a0, 0, -(a0/3), 0, a0/5, 0, -(a0/7), 0, a0/9, 0, -(a0/11), 0,
            a0/13, 0, -(a0/15), 0, a0/17, 0, -(a0/19)},
           {i, {i, 2, 20}}
     ]
]
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I think this does what you want.

list = RecurrenceTable[{a[n + 2] == (1 - n)/(n + 1) a[n], a[2] == a0, a[3] == 0}, 
   a, {n, 2, 20}];

TableForm[{Range[2, 20], list}, TableHeadings -> {{"n", "a[n]"}}, TableDirections -> Row]

For Mathematica versions 10.0, 10.1 or 10.2 add the option TableAlignments -> Center to get around this bug:

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  • $\begingroup$ The specified setting for the option GridBoxOptions, RowAlignments cannot be used. $\endgroup$ – rhermans Feb 16 '16 at 17:28
  • $\begingroup$ @rhermans Yes, which is what I need to look at. It appears to be a bug in TableForm. Nevertheless the output appears correct, no? $\endgroup$ – Mr.Wizard Feb 16 '16 at 17:30
  • 1
    $\begingroup$ @rhermans Turns out it's a known bug I hadn't noticed until today: (95321) $\endgroup$ – Mr.Wizard Feb 16 '16 at 17:32
  • $\begingroup$ You are correct. +1 $\endgroup$ – rhermans Feb 16 '16 at 17:35
  • $\begingroup$ Thanks. Although it gives an error, it works. $\endgroup$ – Zack Fair Feb 16 '16 at 18:00

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