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A277584
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a(n) = binomial(3n-1, n-1)^2.
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1
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0, 1, 25, 784, 27225, 1002001, 38291344, 1502337600, 60101954649, 2440703175625, 100300325150025, 4161829109817600, 174077451630810000, 7330421677037621904, 310467090932230849600, 13214837914326197526784, 564927069263895118093401
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OFFSET
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0,3
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..605
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FORMULA
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a(n) = A025174(n)^2.
a(n) = A188662(n)/9 for n > 0.
Let the number of multisets of length k on n symbols be denoted by ((n, k)) = binomial(n+k-1, k).
a(n) = (Sum_{k=0..n} binomial(n, k)^2 * ((2*n, 2*n - k)))/5 for n > 0.
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MATHEMATICA
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Table[Boole[n > 0] Binomial[3 n - 1, n - 1]^2, {n, 0, 16}] (* Michael De Vlieger, Oct 26 2016 *)
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PROG
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(PARI) a(n) = binomial(3*n-1, n-1)^2; \\ Michel Marcus, Oct 22 2016
(Magma) [Binomial(3*n-1, n-1)^2: n in [0..20]]; // Vincenzo Librandi, Oct 23 2016
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CROSSREFS
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Cf. A025174, A060150, A188662.
Sequence in context: A286439 A123835 A012835 * A223228 A132540 A337247
Adjacent sequences: A277581 A277582 A277583 * A277585 A277586 A277587
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Oct 22 2016
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STATUS
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approved
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