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 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). 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 EXTENSIONS Offset corrected by Reinhard Zumkeller, Mar 19 2014 STATUS approved

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Last modified February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)