A047918 Triangular array read by rows: a(n,k) = Sum_{d|k} mu(d)*U(n,k/d) if k|n else 0, where U(n,k) = A047916(n,k) (1<=k<=n).

1, 2, 0, 6, 0, 0, 8, 0, 0, 16, 20, 0, 0, 0, 100, 12, 24, 36, 0, 0, 648, 42, 0, 0, 0, 0, 0, 4998, 32, 32, 0, 320, 0, 0, 0, 39936, 54, 0, 270, 0, 0, 0, 0, 0, 362556, 40, 160, 0, 0, 3800, 0, 0, 0, 0, 3624800, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39916690, 48, 96

Offset

1,2

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]}]; Flatten[ Table[ a[n, k], {n, 1, 12}, {k, 1, n}]] (* Jean-François Alcover, May 04 2012 *)

Prog

(Haskell)
a047918 n k = sum [a008683 (fromIntegral d) * a047916 n (k `div` d) |
                   mod n k == 0, d <- [1..k], mod k d == 0]
a047918_row n = map (a047918 n) [1..n]
a047918_tabl = map a047918_row [1..]
-- Reinhard Zumkeller, Mar 19 2014

Crossrefs

Cf. A008683, A027750, A225817.

Sequence in context: A346092 A180491 A329893 * A321981 A322481 A262886

Adjacent sequences: A047915 A047916 A047917 * A047919 A047920 A047921

Keyword

nonn,tabl,nice,easy

Author

N. J. A. Sloane

Extensions

Offset corrected by Reinhard Zumkeller, Mar 19 2014

Status

approved