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A047916
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Triangular array read by rows: a(n,k) = phi(n/k)*(n/k)^k*k! if k|n else 0 (1<=k<=n).
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8
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1, 2, 2, 6, 0, 6, 8, 8, 0, 24, 20, 0, 0, 0, 120, 12, 36, 48, 0, 0, 720, 42, 0, 0, 0, 0, 0, 5040, 32, 64, 0, 384, 0, 0, 0, 40320, 54, 0, 324, 0, 0, 0, 0, 0, 362880, 40, 200, 0, 0, 3840, 0, 0, 0, 0, 3628800, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39916800, 48, 144
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.
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LINKS
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EXAMPLE
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1; 2,2; 6,0,6; 8,8,0,24; 20,0,0,0,120; 12,36,48,0,0,720; ...
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MATHEMATICA
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a[n_, k_] := If[Divisible[n, k], EulerPhi[n/k]*(n/k)^k*k!, 0]; Flatten[ Table[ a[n, k], {n, 1, 12}, {k, 1, n}]] (* Jean-François Alcover, May 04 2012 *)
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PROG
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(Haskell)
import Data.List (zipWith4)
a047916 n k = a047916_tabl !! (n-1) !! (k-1)
a047916_row n = a047916_tabl !! (n-1)
a047916_tabl = zipWith4 (zipWith4 (\x u v w -> x * v ^ u * w))
a054523_tabl a002260_tabl a010766_tabl a166350_tabl
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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