A047917 Triangular array read by rows: a(n,k) = phi(n/k)*(n/k)^k*k!/n if k|n else 0 (1<=k<=n).

1, 1, 1, 2, 0, 2, 2, 2, 0, 6, 4, 0, 0, 0, 24, 2, 6, 8, 0, 0, 120, 6, 0, 0, 0, 0, 0, 720, 4, 8, 0, 48, 0, 0, 0, 5040, 6, 0, 36, 0, 0, 0, 0, 0, 40320, 4, 20, 0, 0, 384, 0, 0, 0, 0, 362880, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800, 4, 12, 64, 324, 0, 3840, 0, 0, 0, 0

Offset

1,4

References

J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

C. L. Mallows and N. J. A. Sloane, Notes on A002618, A002619, etc.

N. J. A. Sloane, Notes on A002618, A002619, etc.

J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.

J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61. [Annotated scanned copy. Note that the scanned pages are out of order]

Example

1; 1,1; 2,0,2; 2,2,0,6; 4,0,0,0,24; 2,6,8,0,0,120; ...

Mathematica

a[n_, k_] := If[ Divisible[n, k], EulerPhi[n/k]*(n/k)^k*k!/n, 0]; Flatten[ Table[ a[n, k], {n, 1, 12}, {k, 1, n}]](* Jean-François Alcover, Feb 17 2012 *)

Prog

(Haskell)
a047917 n k = a047917_tabl !! (n-1) !! (k-1)
a047917_row n = a047917_tabl !! (n-1)
a047917_tabl = zipWith (zipWith div) a047916_tabl a002024_tabl
-- Reinhard Zumkeller, Mar 19 2014

Crossrefs

Divide n-th row of A047916 by n.

Row sums give A061417.

Cf. A002024.

Sequence in context: A329321 A334239 A335062 * A144569 A000360 A023556

Adjacent sequences: A047914 A047915 A047916 * A047918 A047919 A047920

Keyword

nonn,tabl,nice,easy

Author

N. J. A. Sloane

Extensions

Offset corrected by Reinhard Zumkeller, Mar 19 2014

Status

approved