%I #15 Jun 24 2017 13:24:13
%S 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,
%T 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,
%U 0,0,0,0,0,0,0,0,0,3628800,4,12,64,324,0,3840,0,0,0,0
%N Triangular array read by rows: a(n,k) = phi(n/k)*(n/k)^k*k!/n if k|n else 0 (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="/A047917/b047917.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]
%e 1; 1,1; 2,0,2; 2,2,0,6; 4,0,0,0,24; 2,6,8,0,0,120; ...
%t 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 *)
%o (Haskell)
%o a047917 n k = a047917_tabl !! (n-1) !! (k-1)
%o a047917_row n = a047917_tabl !! (n-1)
%o a047917_tabl = zipWith (zipWith div) a047916_tabl a002024_tabl
%o -- _Reinhard Zumkeller_, Mar 19 2014
%Y Divide n-th row of A047916 by n.
%Y Row sums give A061417.
%Y Cf. A002024.
%K nonn,tabl,nice,easy
%O 1,4
%A _N. J. A. Sloane_
%E Offset corrected by _Reinhard Zumkeller_, Mar 19 2014