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%I #15 May 26 2017 23:31:18
%S 1,1,1,1,4,1,1,11,9,1,1,26,50,16,1,1,57,222,150,25,1,1,120,867,1080,
%T 355,36,1,1,247,3123,6627,3775,721,49,1,1,502,10660,36552,33502,10626,
%U 1316,64,1,1,1013,35064,187000,262570,128758,25676,2220,81,1
%N Square array read by antidiagonals: T(n,k) = sum of unimodal products of length n and bound k.
%C A unimodal product of length n and parameter k is a product of positive integers a_1 ... a_m ... a_n where a_1 <= ... <= a_m <= k and k >= a_m >= ... >= a_n; furthermore we consider each choice of m to give a distinct product, unless a_m=k. (See the example.)
%F T(n,k) is the coefficient of x^n in 1/((1-kx)(1-(k-1)x)^2...(1-x)^2).
%e T(2,3)=50 because of the products 1*1,1*1,1*1 [m=0,1,2]; 1*2,1*2 [m=1,2]; 1*3; 2*1,2*1 [m=0,1]; 2*2,2*2,2*2 [m=0,1,2]; 2*3; 3*1; 3*2; 3*3; total 50.
%t f[k_]:=Product[1-j x,{j,k}]; T[n_,k_]:=Coefficient[Series[1/f[k]/f[k-1],{x,0,n}],x,n]
%Y Cf. A000290, A000295, A222993, A223069.
%K nonn,tabl
%O 0,5
%A _Don Knuth_, May 26 2017
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