A120476 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.

1, 3, -2, 6, -5, -9, 10, -9, -21, -20, 15, -14, -36, -45, -35, 21, -20, -54, -75, -77, -54, 28, -27, -75, -110, -126, -117, -77, 36, -35, -99, -150, -182, -189, -165, -104, 45, -44, -126, -195, -245, -270, -264, -221, -135, 55, -54, -156, -245, -315, -360, -374, -351, -285, -170

Offset

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..54.

Formula

a(n,m) = (2n-1)*[A000217(n)-A000217(m)] = (1-2n)*A049777(n,m) . - R. J. Mathar, Dec 05 2007

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]

Example

1,
3, -2,
6, -5, -9,
10, -9, -21,-20,
15, -14,-36,-45, -35

Mathematica

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]

Crossrefs

Cf. A006472.

Sequence in context: A046877 A067587 A198259 * A069159 A306389 A255548

Adjacent sequences: A120473 A120474 A120475 * A120477 A120478 A120479

Keyword

sign,tabl

Author

Roger L. Bagula, Jul 19 2006

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

Status

approved