OFFSET
0,25
COMMENTS
LINKS
Mohammad Torabi-Dashti, Faulhaber’s Triangle [Annotated scanned copy of preprint]
Mohammad Torabi-Dashti, Faulhaber's Triangle, College Math. J., 42:2 (2011), 96-97.
Eric Weisstein's MathWorld, Power Sum
EXAMPLE
Rows start:
0,1;
0,1,1;
0,1,1,1;
0,0,1,1,1;
0,-1,0,1,1,1;
0,0,-1,0,5,1,1;
0,1,0,-1,0,1,1,1;
0,0,1,0,-7,0,7,1,1;
0,-1,0,2,0,-7,0,2,1,1;
...
MATHEMATICA
f[n_, x_] := f[n, x]=((x + 1)^(n + 1) - 1)/(n + 1) - Sum[Binomial[n + 1, k]*f[k, x], {k , 0, n - 1}]/(n + 1); f[0, x_] := x; row[n_] := CoefficientList[f[n, x], x] // Numerator; Table[row[n], {n, 0, 10}] // Flatten
CROSSREFS
KEYWORD
sign,tabf,frac
AUTHOR
Jean-François Alcover, Dec 27 2012
STATUS
approved