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A219560
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Number of tripartite partitions of (n,n,n) into distinct triples.
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6
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1, 5, 40, 364, 2897, 21369, 148257, 970246, 6032341, 35850410, 204646488, 1126463948, 5999145787, 30999381232, 155798366059, 763194776551, 3650648583934, 17079277343463, 78262895082681, 351708874155894, 1551843168854346
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OFFSET
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0,2
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COMMENTS
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Number of factorizations of (p*q*r)^n into distinct factors where p, q, r are distinct primes.
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LINKS
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FORMULA
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a(n) = [(x*y*z)^n] 1/2 * Product_{i,j,k>=0} (1+x^i*y^j*z^k).
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EXAMPLE
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a(0) = 1: [].
a(1) = 5: [(1,1,1)], [(1,1,0),(0,0,1)], [(1,0,1),(0,1,0)], [(0,1,1),(1,0,0)], [(0,0,1),(0,1,0),(1,0,0)].
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MAPLE
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with(numtheory):
b:= proc(n, k) option remember;
`if`(n>k, 0, 1) +`if`(isprime(n), 0,
add(`if`(d>k, 0, b(n/d, d-1)), d=divisors(n) minus {1, n}))
end:
a:= n-> b(30^n$2):
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n > k, 0, 1] + If[PrimeQ[n], 0, Sum[If[d > k, 0, b[n/d, d - 1]], {d, Divisors[n][[2 ;; -2]]}]]; a[0] = 1; a[n_] := b[30^n, 30^n]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* Jean-François Alcover, Jan 15 2016, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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