A220963 Faulhaber’s triangle: triangle of denominators of coefficients of power-sum polynomials.

1, 1, 1, 2, 2, 1, 6, 2, 3, 1, 1, 4, 2, 4, 1, 30, 1, 3, 2, 5, 1, 1, 12, 1, 12, 2, 6, 1, 42, 1, 6, 1, 2, 2, 7, 1, 1, 12, 1, 24, 1, 12, 2, 8, 1, 30, 1, 9, 1, 15, 1, 3, 2, 9, 1, 1, 20, 1, 2, 1, 10, 1, 4, 2, 10, 1, 66, 1, 2, 1, 1, 1, 1, 1, 6, 2, 11

Offset: 0

Author

Jean-François Alcover, Dec 27 2012

Keywords

• nonn
• tabf
• frac

Comments

This version of Faulhaber's triangle, A220962/A220963, is essentially the same as A162298/A162299 except for having an extra column of 0's. See A162298/A162299 for further information. - N. J. A. Sloane, Jan 28 2017

Examples

			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;
...
		

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

Crossrefs

Cf. A220962 (numerators).

See also A162298/A162299.

Programs

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