OFFSET
0,4
COMMENTS
Changing the initial conditions in the recursion produces a different triangular sequence. The result here is a variation of Stirling's numbers of the first kind. The Chang and Sederberg version of this recursion produces an even function in sections.
REFERENCES
Chang and Sederberg, Over and Over Again, MAA, 1997, page 209 (Moving Averages).
LINKS
G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
EXAMPLE
Triangle begins:
1;
1, 1;
2, 1, -1;
6, 1, -4, 1;
24, -2, -17, 8, -1;
120, -34, -83, 57, -13, 1;
720, -324, -464, 425, -135, 19, -1;
5040, -2988, -2924, 3439, -1370, 268, -26, 1;
MAPLE
p[0]:=1: p[1]:=1+x: for n from 2 to 10 do p[n]:=sort(expand((n-x)*p[n-1])) od: for n from 0 to 10 do seq(coeff(p[n], x, k), k=0..n) od; # yields sequence in triangular form
MATHEMATICA
p[ -1, x] = 1; p[0, x] = x + 1; p[k_, x_] := p[k, x] = (-x + k + 1)*p[k - 1, x] w = Table[CoefficientList[p[n, x], x], {n, -1, 10}]; Flatten[w]
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Nov 09 2006
EXTENSIONS
Edited by N. J. A. Sloane, Nov 24 2006, Jun 17 2007
STATUS
approved