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%I #16 Jun 24 2017 20:05:18
%S 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,
%T 32,32,0,320,0,0,0,39936,54,0,270,0,0,0,0,0,362556,40,160,0,0,3800,0,
%U 0,0,0,3624800,110,0,0,0,0,0,0,0,0,0,39916690,48,96
%N 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).
%D J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.
%H Reinhard Zumkeller, <a href="/A047918/b047918.txt">Rows n = 1..125 of triangle, flattened</a>
%H C. L. Mallows and N. J. A. Sloane, <a href="/A002618/a002618_1.pdf">Notes on A002618, A002619, etc.</a>
%H N. J. A. Sloane, <a href="/A002618/a002618_2.pdf">Notes on A002618, A002619, etc.</a>
%H J. E. A. Steggall, <a href="http://www.handweaving.net/DAItemDetail.aspx?ItemID=3237">On the numbers of patterns which can be derived from certain elements</a>, Mess. Math., 37 (1907), 56-61.
%H J. E. A. Steggall, <a href="/A002618/a002618.pdf">On the numbers of patterns which can be derived from certain elements</a>, Mess. Math., 37 (1907), 56-61. [Annotated scanned copy. Note that the scanned pages are out of order]
%t 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 *)
%o (Haskell)
%o a047918 n k = sum [a008683 (fromIntegral d) * a047916 n (k `div` d) |
%o mod n k == 0, d <- [1..k], mod k d == 0]
%o a047918_row n = map (a047918 n) [1..n]
%o a047918_tabl = map a047918_row [1..]
%o -- _Reinhard Zumkeller_, Mar 19 2014
%Y Cf. A008683, A027750, A225817.
%K nonn,tabl,nice,easy
%O 1,2
%A _N. J. A. Sloane_
%E Offset corrected by _Reinhard Zumkeller_, Mar 19 2014
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