A136457 - OEIS

%I #8 Jul 05 2018 09:18:02

%S 1,-1,1,1,-2,1,-2,5,-4,1,12,-32,29,-10,1,-288,780,-728,269,-34,1,

%T 34560,-93888,88140,-33008,4349,-154,1,-24883200,67633920,-63554688,

%U 23853900,-3164288,115229,-874,1,125411328000,-340899840000,320383261440,-120287210688,15971865420,-583918448,4520189

%N Triangle read by rows: coefficients of polynomials defined by recursion p(x,n)=(x-Gamma(n))*p(x,n-1).

%C These are inspired by Cornelius-Schultz matrices.

%C Row sums are: {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}

%H E. F. Cornelius and Phill Schultz, <a href="https://www.jstor.org/stable/27642423">Sequences Generated by Polynomials</a>, Amer. Math. Monthly, No. 2, 2008.

%F p(x,0)=1; p(x,1)=x-1; p(x,n)=(x-Gamma(n))*p(x,n-1)

%e Triangle begins:

%e {1},

%e {-1, 1},

%e {1, -2, 1},

%e {-2, 5, -4, 1},

%e {12, -32, 29, -10, 1},

%e {-288, 780, -728, 269, -34, 1},

%e {34560, -93888, 88140, -33008, 4349, -154, 1}

%t Clear[p, x, n, a] p[x, 0] = 1; p[x, 1] = x - 1; p[x_, m_] := p[x, n] = (x - Gamma[n])*p[x, n - 1]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]; Table[ExpandAll[p[x, n]], {n, 0, 10}];

%K tabl,sign

%O 1,5

%A _Roger L. Bagula_, Mar 20 2008

%E Edited by _N. J. A. Sloane_, Aug 10 2008