A269942 Triangle read by rows, the coefficients of the inverse partial P-polynomials.

1, 0, -1, 0, -1, 1, 0, -2, 1, 2, -1, 0, -5, 5, -1, 5, -2, -3, 1, 0, -14, 21, -3, -6, 1, 14, -12, 2, -9, 3, 4, -1, 0, -42, 84, -28, -28, 7, 7, -1, 42, -56, 7, 14, -2, -28, 21, -3, 14, -4, -5, 1

Offset

0,8

Comments

The triangle of coefficients of the partial P-polynomials is A269941. For the definition of the inverse partial P-polynomials see the link 'P-transform'.

Links

Table of n, a(n) for n=0..51.

Peter Luschny, The P-transform.

Example

[[1]],
[[0], [-1]],
[[0], [-1], [1]],
[[0], [-2, 1], [2], [-1]],
[[0], [-5, 5, -1], [5, -2], [-3], [1]],
[[0], [-14, 21, -3, -6, 1], [14, -12, 2], [-9, 3], [4], [-1]],
[[0], [-42,84,-28,-28,7,7,-1],[42,-56,7,14,-2],[-28,21,-3],[14,-4],[-5],[1]]
Replacing the sublists by their sums reduces the triangle to a signed version of the triangle A097805. The column 1 of sublists is A111785 in a different order.

Prog

(Sage)
# For function PMultiCoefficients see A269941.
PMultiCoefficients(7, inverse = True)

Crossrefs

Cf. A097805, A111785, A268441, A268442, A269941.

Sequence in context: A240159 A309447 A320312 * A094645 A105793 A373429

Adjacent sequences: A269939 A269940 A269941 * A269943 A269944 A269945

Keyword

sign,tabf,changed

Author

Peter Luschny, Mar 08 2016

Status

approved