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A162995 A scaled version of triangle A162990.

%I A162995 #20 Mar 31 2024 19:16:04
%S A162995 1,3,1,12,4,1,60,20,5,1,360,120,30,6,1,2520,840,210,42,7,1,20160,6720,
%T A162995 1680,336,56,8,1,181440,60480,15120,3024,504,72,9,1,1814400,604800,
%U A162995 151200,30240,5040,720,90,10,1
%N A162995 A scaled version of triangle A162990.
%C A162995 We get this scaled version of triangle A162990 by dividing the coefficients in the left hand columns by their 'top-values' and then taking the square root.
%C A162995 T(n,k) = A173333(n+1,k+1), 1 <= k <= n. - _Reinhard Zumkeller_, Feb 19 2010
%C A162995 T(n,k) = A094587(n+1,k+1), 1 <= k <= n. - _Reinhard Zumkeller_, Jul 05 2012
%H A162995 Reinhard Zumkeller, <a href="/A162995/b162995.txt">Rows n = 1..150 of triangle, flattened</a>
%F A162995 a(n,m) = (n+1)!/(m+1)! for n = 1, 2, 3, ..., and m = 1, 2, ..., n.
%e A162995 The first few rows of the triangle are:
%e A162995 [1]
%e A162995 [3, 1]
%e A162995 [12, 4, 1]
%e A162995 [60, 20, 5, 1]
%p A162995 a := proc(n, m): (n+1)!/(m+1)! end: seq(seq(a(n, m), m=1..n), n=1..9); # _Johannes W. Meijer_, revised Nov 23 2012
%t A162995 Table[(n+1)!/(m+1)!, {n, 10}, {m, n}] (* _Paolo Xausa_, Mar 31 2024 *)
%o A162995 (Haskell)
%o A162995 a162995 n k = a162995_tabl !! (n-1) !! (k-1)
%o A162995 a162995_row n = a162995_tabl !! (n-1)
%o A162995 a162995_tabl = map fst $ iterate f ([1], 3)
%o A162995    where f (row, i) = (map (* i) row ++ [1], i + 1)
%o A162995 -- _Reinhard Zumkeller_, Jul 04 2012
%Y A162995 Cf. A094587.
%Y A162995 A056542(n) equals the row sums for n>=1.
%Y A162995 A001710, A001715, A001720, A001725, A001730, A049388, A049389, A049398, A051431 are related to the left hand columns.
%Y A162995 A000012, A009056, A002378, A007531, A052762, A052787, A053625 and A159083 are related to the right hand columns.
%K A162995 easy,nonn,tabl
%O A162995 1,2
%A A162995 _Johannes W. Meijer_, Jul 27 2009