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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.
0
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
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
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Jul 19 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 01 2006
STATUS
approved