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A171522
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Denominator of 1/n^2-1/(n+2)^2.
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8
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0, 9, 16, 225, 144, 1225, 576, 3969, 1600, 9801, 3600, 20449, 7056, 38025, 12544, 65025, 20736, 104329, 32400, 159201, 48400, 233289, 69696, 330625, 97344, 455625, 132496, 613089, 176400, 808201, 230400, 1046529, 295936, 1334025, 374544, 1677025, 467856
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OFFSET
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0,2
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COMMENTS
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This is the third column in the table of denominators of the hydrogenic spectra (the main diagonal A147560):
1, 4, 9, 16, 25, 36, 49, 64... A000290
1, 36, 16, 100, 9, 196, 64, 324... A061038
1, 144, 225, 12, 441, 576, 81, 900... A061040
1, 400, 144, 784, 64,1296, 400,1936... A061042
1, 900 1225,1600,2025, 100,3025,3600... A061044
1,1764, 576, 324, 225,4356, 48,6084... A061046
1,3136,3969,4900,5929,7056,8281, 196... A061048.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,0,1).
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FORMULA
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a(n) = -((-5+3*(-1)^n)*n^2*(2+n)^2)/8. - Colin Barker, Nov 05 2014
G.f.: x*(x^8+4*x^6+16*x^5+190*x^4+64*x^3+180*x^2+16*x+9) / ((x-1)^5*-(x+1)^5). - Colin Barker, Nov 05 2014
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MAPLE
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A171522 := proc(n) if n = 0 then 0 else lcm(n+2, n) ; %^2 ; end if ; end:
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MATHEMATICA
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a[n_] := If[EvenQ[n], (n*(n+2))^2/4, (n*(n+2))^2]; Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Jun 13 2017 *)
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PROG
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(PARI) concat(0, Vec(x*(x^8+4*x^6+16*x^5+190*x^4+64*x^3+180*x^2+16*x+9) / ((x-1)^5*-(x+1)^5) + O(x^100))) \\ Colin Barker, Nov 05 2014
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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