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A085740
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T(n)^2-n^2, where T(n) is a triangular number.
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2
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0, 0, 5, 27, 84, 200, 405, 735, 1232, 1944, 2925, 4235, 5940, 8112, 10829, 14175, 18240, 23120, 28917, 35739, 43700, 52920, 63525, 75647, 89424, 105000, 122525, 142155, 164052, 188384, 215325, 245055, 277760, 313632, 352869, 395675, 442260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the dimension of the second Cartan power of sl(n, C), which is the irreducible representation of sl(n, C) the highest weight of which is twice that of the adjoint representation. - Daniel Fox (fox(AT)math.gatech.edu), Jan 01 2006.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n) = n^2*(n^2+2*n-3)/4.
a(n) = A000096(n)*A000217(n-1).
a(n) = 4*A173963(n+1). - Reinhard Zumkeller, Mar 03 2010
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EXAMPLE
| a(3)=T(3)^2-3^2=6^2-9=36-9=27
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PROG
| (PARI) for(n=0, 50, print1(n^2*(n^2-9)/4", "))
(MAGMA)[n^2*(n^2+2*n-3)/4: n in [0..40]]; // Vincenzo Librandi, Sep 09 2011
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CROSSREFS
| Cf. A000096, A000217; A173963.
Sequence in context: A137117 A064675 A135713 * A201436 A202508 A129868
Adjacent sequences: A085737 A085738 A085739 * A085741 A085742 A085743
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KEYWORD
| nonn,easy
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Jul 21 2003
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