A095873 - OEIS

%I #16 May 03 2018 15:22:44

%S 1,4,9,9,24,25,16,45,60,49,25,72,105,112,81,36,105,160,189,180,121,49,

%T 144,225,280,297,264,169,64,189,300,385,432,429,364,225,81,240,385,

%U 504,585,616,585,480,289,100,297,480,637,756,825

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

%C Matrix square of A158405.

%D Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966.

%F T(n,k) = (2*k-1)*A094728(n,k).

%F 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 [1 0 0 / 1 3 0 / 1 3 5]^2 = [1 0 0 / 4 9 0 / 9 24 25]. Delete the zeros and

%e read by rows:

%e 1;

%e 4, 9;

%e 9, 24, 25;

%e 16,45, 60, 49;

%e 25,72,105,112, 81;

%p A095873 := proc(n,k)

%p         (2*k-1)*(n+k-1)*(n-k+1) ;

%p end proc:

%p seq(seq(A095873(n,k),k=1..n),n=1..13) ; # _R. J. Mathar_, Oct 30 2011

%t Table[(2k-1)(n+k-1)(n-k+1),{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, May 03 2018 *)

%Y Cf. A094728, A095871, A095872.

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Jun 10 2004

%E Definition in closed form by _R. J. Mathar_, Oct 30 2011