A120476 - OEIS

%I #11 Mar 12 2014 16:36:53

%S 1,3,-2,6,-5,-9,10,-9,-21,-20,15,-14,-36,-45,-35,21,-20,-54,-75,-77,

%T -54,28,-27,-75,-110,-126,-117,-77,36,-35,-99,-150,-182,-189,-165,

%U -104,45,-44,-126,-195,-245,-270,-264,-221,-135,55,-54,-156,-245,-315,-360,-374,-351,-285,-170

%N Triangle read by rows: a(n,m)=(2*n-1)*(n-m)*(n+m+1)/2, where n is the column and m the row index.

%C Triangular array based on recurrence in Laplace function in J. W. S. Rayleigh.

%D J. W. S. Rayleigh, The Theory of Sound, volume 2, page 237,Dover, New York,1945

%F a(n,m) = (2n-1)*[A000217(n)-A000217(m)] = (1-2n)*A049777(n,m) . - _R. J. Mathar_, Dec 05 2007

%F Row sums: sum_{n=0..m-1} a(n,m) = -m(m+1)(3m^2-5m-4)/12. [From _R. J. Mathar_, Jan 15 2009]

%e 1,

%e 3, -2,

%e 6, -5, -9,

%e 10, -9, -21,-20,

%e 15, -14,-36,-45, -35

%t a = Table[Table[(m + 1)*(2*n - 1)*(n - m)*(n + m + 1)/(2*(m + 1)), {n, 0, m - 1}], {m, 1, 10}] Flatten[a]

%Y Cf. A006472.

%K sign,tabl

%O 0,2

%A _Roger L. Bagula_, Jul 19 2006

%E Edited by _N. J. A. Sloane_, Oct 01 2006