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

0,4

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).

See also A162298/A162299.

Sequence in context: A371886 A280245 A290013 * A179313 A209692 A178886

Adjacent sequences: A220960 A220961 A220962 * A220964 A220965 A220966

Keyword

nonn,tabf,frac

Author

Jean-François Alcover, Dec 27 2012

Status

approved