[seqfan] Re: A025597 computation

[Wouter Meeussen]

yes, the result fits all 23 known terms; extension to 48 :

Table[4/81*
      Sum[(-1)^(j + k)  *
          Sin[j*Pi/9]^2  Sin[
              k*Pi/9]^2 *  ((1 + 2Cos[j*Pi/9])*(1 + 2Cos[k*Pi/9]) - 1)^n , 
{j,
           8}, {k, 8}], {n, 48}];

Round[ N[%, 64] ]

{0, 0, 0, 0, 0, 0, 1, 56, 1309, 20370, 255366, 2782296, 27630317, 256617790,
2269878170, 19345170656, 160223380546, 1297456951652, 10319966008680,
80906898257760, 626886465395595, 4810654849509082, 36623649326935517,
276978367797824968, 2083200939963715126, 15595683813101279420,
116301107197615295905, 864435471139653592500, 6407217503910893277444,
47378067330093217182600, 349630722268949591264588, 
2575700394882062294904448,
18947140880906832557051456, 139202483079923884540608128,
1021606539041179715511956893, 7490666332544968034191929020,
54880014410659600034779737717, 401803308907807919979966340230,
2940084653973218884807223098446, 21502488469368326228248902945424,
157192063747654277121963377183669, 1148713224897468635134162828539394,
8391781153727818906899077746007038, 61288282367565060553519666623733112,
447505180064735246955442905726814174, 3266857758785435955732406250575642164,
23844387150444635926903104779107943592,
174010885751792255799158735894761920384}

Wouter


-----Original Message----- 
From: David Wilson
Sent: Sunday, June 24, 2012 4:19 PM
To: Sequence Fanatics
Subject: [seqfan] A025597 computation

I have been sent the following ostensible formula for A025597.
*
f(n) = (4/81) * sum(j=1...8, k=1...8) [(-1)^(j+k)] *
[sin(j*pi/9)*sin(k*pi/9)]^2 * [(1+2cos(j*pi/9))*(1+2cos(k*pi/9))-1]^n

*Could someone with power tools kindly verify a few terms?
*
*

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