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A095873 Triangle T(n,k) = (2*k-1)*(n+k-1)*(n-k+1) read by rows, 1<=k<=n.

%I A095873 #16 May 03 2018 15:22:44
%S A095873 1,4,9,9,24,25,16,45,60,49,25,72,105,112,81,36,105,160,189,180,121,49,
%T A095873 144,225,280,297,264,169,64,189,300,385,432,429,364,225,81,240,385,
%U A095873 504,585,616,585,480,289,100,297,480,637,756,825
%N A095873 Triangle T(n,k) = (2*k-1)*(n+k-1)*(n-k+1) read by rows, 1<=k<=n.
%C A095873 Matrix square of A158405.
%D A095873 Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966.
%F A095873 T(n,k) = (2*k-1)*A094728(n,k).
%F A095873 Sum_{k=1..n} T(n,k)= n*(n+1)*(3*n^2+n-1)/6 = A103220(n). - _R. J. Mathar_, Oct 30 2011
%e A095873 [1 0 0 / 1 3 0 / 1 3 5]^2 = [1 0 0 / 4 9 0 / 9 24 25]. Delete the zeros and
%e A095873 read by rows:
%e A095873 1;
%e A095873 4, 9;
%e A095873 9, 24, 25;
%e A095873 16,45, 60, 49;
%e A095873 25,72,105,112, 81;
%p A095873 A095873 := proc(n,k)
%p A095873         (2*k-1)*(n+k-1)*(n-k+1) ;
%p A095873 end proc:
%p A095873 seq(seq(A095873(n,k),k=1..n),n=1..13) ; # _R. J. Mathar_, Oct 30 2011
%t A095873 Table[(2k-1)(n+k-1)(n-k+1),{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, May 03 2018 *)
%Y A095873 Cf. A094728, A095871, A095872.
%K A095873 nonn,tabl,easy
%O A095873 1,2
%A A095873 _Gary W. Adamson_, Jun 10 2004
%E A095873 Definition in closed form by _R. J. Mathar_, Oct 30 2011