OFFSET
1,4
COMMENTS
Row sums: {1, 1, 0, -3, -18, -129, -1182, -13281, -176478, -2704119, -46909362, ...}.
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1972, 10th edition, (and various reprintings), p. 631.
LINKS
G. C. Greubel, Table of n, a(n) for the first 25 rows, flattened
FORMULA
P(x,0) = 1; P(x,1) = 1/x; P(x, n) = 2*(n-1)*P(x, n - 1)/x - n*P(x, n - 2); with substitution of x to 1/y.
EXAMPLE
Triangle begins as:
1;
0, 1;
-2, 0, 2;
0, -11, 0, 8;
8, 0, -74, 0, 48;
0, 119, 0, -632, 0, 384;
-48, 0, 1634, 0, -6608, 0, 3840;
0, -1409, 0, 24032, 0, -81984, 0, 46080;
....
MATHEMATICA
P[x, 0]= 1; P[x, 1]= 1/x;
P[x_, n_]:= P[x, n] = 2*(n-1)*P[x, n-1]/x - n*P[x, n-2];
Table[ExpandAll[P[x, n] /. x -> 1/y], {n, 0, 10}];
Table[CoefficientList[P[x, n] /. x -> 1/y, y], {n, 0, 10}]//Flatten
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Apr 03 2008
STATUS
approved