A220963 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

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

LINKS

Table of n, a(n) for n=0..76.

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

Cf. A220962 (numerators).