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A062206
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a(n) = n^(2n).
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22
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1, 1, 16, 729, 65536, 9765625, 2176782336, 678223072849, 281474976710656, 150094635296999121, 100000000000000000000, 81402749386839761113321, 79496847203390844133441536, 91733330193268616658399616009
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OFFSET
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0,3
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COMMENTS
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a(n) is also the number of sequences of length 2n on n symbols. - Washington Bomfim, Oct 06 2009
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 0..100
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FORMULA
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a(n) = A000312(n)^2.
(-1)^n*determinant of the 2n X 2n matrix M_(i, j) = i+j if (i + j) is a multiple of n, M_(i, j) = 1 otherwise. - Benoit Cloitre, Aug 06 2003
a(n) = A155955(n,n) = A000290(A000312(n)). - Reinhard Zumkeller, Jan 31 2009
a(n) = n! * [x^n] 1/(1 + LambertW(-n*x)). - Ilya Gutkovskiy, Oct 03 2017
Sum_{n>=1} 1/a(n) = A086648. - Amiram Eldar, Nov 16 2020
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MATHEMATICA
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f[n_]:=n^(2*n); Join[{1}, f[Range[20]]] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
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PROG
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(PARI) a(n) = n^(2*n); \\ Harry J. Smith, Aug 02 2009
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CROSSREFS
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Cf. A062207, A086648, A155957.
Cf. A000312, A085741, A212333.
Column k=0 of A245910 and A245980.
Sequence in context: A220809 A221023 A171736 * A209537 A086701 A218297
Adjacent sequences: A062203 A062204 A062205 * A062207 A062208 A062209
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KEYWORD
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easy,nonn
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AUTHOR
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Jason Earls, Jun 13 2001
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EXTENSIONS
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Initial term corrected by Reinhard Zumkeller, Jan 30 2009
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STATUS
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approved
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