%I #32 Feb 01 2023 12:27:41
%S 1,2,0,3,1,0,4,1,0,0,5,2,1,0,0,6,2,1,0,0,0,7,3,1,1,0,0,0,8,3,2,1,0,0,
%T 0,0,9,4,2,1,1,0,0,0,0,10,4,2,1,1,0,0,0,0,0,11,5,3,2,1,1,0,0,0,0,0,12,
%U 5,3,2,1,1,0,0,0,0,0,0,13,6,3,2,1,1,1,0,0,0,0,0,0,14,6,4,2,2,1,1,0,0,0,0
%N Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is [ i/j ].
%C Another version of A010766.
%H Reinhard Zumkeller, <a href="/A003988/b003988.txt">Table of n, a(n) for n = 1..5050</a>
%F From _Franklin T. Adams-Watters_, Jan 28 2006: (Start)
%F T(n,k) = Sum_{i=1..k} A077049(n,i).
%F G.f.: (1/(1-x))*Sum_{k>0} x^k*y^k/(1-x^k) = (1/(1-x))*Sum_{k>0} x^k * y / (1 - x^k y) = (1/(1-x)) * Sum_{k>0} x^k * Sum_{d|k} y^d = A(x,y)/(1-x) where A(x,y) is the g.f. of A077049. (End)
%F T(n,k) = floor((n + 1 - k) / k). - _Reinhard Zumkeller_, Apr 13 2012
%t t[n_, k_] := Quotient[n, k]; Table[t[n-k+1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Nov 21 2013 *)
%o (Haskell)
%o a003988 n k = (n + 1 - k) `div` k
%o a003988_row n = zipWith div [n,n-1..1] [1..n]
%o a003988_tabl = map a003988_row [1..]
%o -- _Reinhard Zumkeller_, Apr 13 2012
%Y Cf. A010766, A003056, A049581, A003991, A004247, A077049.
%Y Row sums are in A006218. Antidiagonal sums are in A002541.
%K tabl,nonn,easy,nice
%O 1,2
%A _Marc LeBrun_
%E More terms from _James A. Sellers_