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 A051683 Triangle read by rows: a(n,k)=n!*k. 9

%I

%S 1,2,4,6,12,18,24,48,72,96,120,240,360,480,600,720,1440,2160,2880,

%T 3600,4320,5040,10080,15120,20160,25200,30240,35280,40320,80640,

%U 120960,161280,201600,241920,282240,322560,362880,725760,1088640,1451520

%N Triangle read by rows: a(n,k)=n!*k.

%C Numbers with only one non-zero digit when written in base factorial. - Franklin T. Adams-Watters, Nov 28 2011.

%H _Reinhard Zumkeller_, <a href="/A051683/b051683.txt">Rows n=1..150 of triangle, flattened</a>

%H Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Inversion_%28discrete_mathematics%29#arrays4">Arrays of permutations</a>

%e Table begins

%e 1

%e 2 4

%e 6 12 18

%e 24 48 72 96 ...

%t a[n_, k_] := n!*k; Flatten[Table[a[n, k], {n, 9}, {k, n}]] (* From Jean-François Alcover, Apr 22 2011 *)

%o a051683 n k = a051683_tabl !! (n-1) !! (k-1)

%o a051683_row n = a051683_tabl !! (n-1)

%o a051683_tabl = map fst \$ iterate f ([1], 2) where

%o f (row, n) = (row' ++ [head row' + last row'], n + 1) where

%o row' = map (* n) row

%o -- _Reinhard Zumkeller_, Mar 09 2012

%Y Cf. A000142, row sums give A001286(n+1).

%Y Cf. A200748.

%Y Cf. A162608.

%K easy,nice,nonn,tabl

%O 1,2

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)

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