A047919 Triangular array read by rows: a(n,k) = Sum_{d|k} mu(d)*U(n,k/d)/n if k|n else 0, where U(n,k) = A047916(n,k) (1<=k<=n).

1, 1, 0, 2, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 20, 2, 4, 6, 0, 0, 108, 6, 0, 0, 0, 0, 0, 714, 4, 4, 0, 40, 0, 0, 0, 4992, 6, 0, 30, 0, 0, 0, 0, 0, 40284, 4, 16, 0, 0, 380, 0, 0, 0, 0, 362480, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3628790, 4, 8, 60, 312, 0, 3768, 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]

Mathematica

U[n_, k_] := If[Divisible[n, k], EulerPhi[n/k]*(n/k)^k*k!, 0]; a[n_, k_] := Sum[If[Divisible[n, k], MoebiusMu[d]*U[n, k/d], 0], {d, Divisors[k]}]; row[n_] := Table[a[n, k], {k, 1, n}]/n; Table[row[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Nov 21 2012, after A047918 *)

Prog

(Haskell)
a047919 n k = a047919_tabl !! (n-1) !! (k-1)
a047919_row n = a047919_tabl !! (n-1)
a047919_tabl = zipWith (zipWith div) a047918_tabl a002024_tabl
-- Reinhard Zumkeller, Mar 19 2014

Crossrefs

Divide n-th row of array A047918 by n.

Cf. A002024.

Sequence in context: A138805 A316400 A061897 * A272624 A271223 A260944

Adjacent sequences: A047916 A047917 A047918 * A047920 A047921 A047922

Keyword

nonn,tabl,nice,easy

Author

N. J. A. Sloane

Extensions

Offset corrected by Reinhard Zumkeller, Mar 19 2014

Status

approved