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A171522
Denominator of 1/n^2-1/(n+2)^2.
8
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
OFFSET
0,2
COMMENTS
This is the third column in the table of denominators of the hydrogenic spectra (the main diagonal A147560):
0, 0, 0, 0, 0, 0, 0, 0... A000004
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.
FORMULA
a(n) = (A066830(n+1))^2.
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
MAPLE
A171522 := proc(n) if n = 0 then 0 else lcm(n+2, n) ; %^2 ; end if ; end:
seq(A171522(n), n=0..70) ; # R. J. Mathar, Dec 15 2009
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A105371. Bisections: A060300, A069075.
Sequence in context: A075373 A072470 A053911 * A236287 A329964 A050802
KEYWORD
nonn,easy,frac
AUTHOR
Paul Curtz, Dec 11 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Dec 15 2009
STATUS
approved