[seqfan] Re: A series for exp(Pi)

[Simon Plouffe]

about :

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Dear Seqfans,

http://research.att.com/~njas/sequences/A166748
has a(0)=1, a(1)=6 and a(n)=(40-4*n+n2)*a(n-2) for n>=2.
( See http://research.att.com/~njas/sequences/A039661 )

Maybe I should already know, but... how is the closed form of this
kind of recurrences found?
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Hello

  the sequence is easily cracked by gfun,

[1, 6, 36, 222, 1440, 9990, 74880, 609390, 5391360, 51798150, 539136000, 
6060383550, 73322496000, 951480217350, 13198049280000, 195053444556750,


     3061947432960000, 50908949029311750, 894088650424320000, 
16545408434526318750, 321871914152755200000, 6568527148506948543750,

     140336154570601267200000, 3133187449837814455368750, 
72974800376712658944000000, 1770250909158365167283343750,

     44660577830548147273728000000, 1170135850953679375574290218750, 
31798331415350280858894336000000, 895153925979564722314332017343750,

     26074631760587230304293355520000000, 
785049993084078261469669179210468750, 
24405855327909647564818580766720000000,

     782694843104826026685260171672837343750, 
25870206647584226418707695612723200000000, 
880531698492929280020917693131942011718750,

     30837286323920397891099573170366054400000000, 
1110350471799583822106377211039378876777343750,

     41075265383461969990944631462927584460800000000, 
1560042412878415270059459981510327321872167968750,

     60791392767523715586598054565132825001984000000000, 
2428986036851692575482579191211579640154965527343750,

     99454718567668798699674417268557301703245824000000000, 
4170569025274356152103588471310282242146075810449218750]

 > listtorec(%,a(n));
                     2      3                          2    3
[{(216 + 216 n + 6 n  + 6 n ) a(n) + (111 + 43 n + 5 n  + n ) a(n + 1) + 
(-6 - 6 n) a(n + 2) + (-n - 3) a(n + 3), 1 = 6, 6 = 36, a(0) = 1}, ogf

     ]

simon plouffe