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 A136457 Triangle read by rows: coefficients of polynomials defined by recursion p(x,n)=(x-Gamma(n))*p(x,n-1). 0
 1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 12, -32, 29, -10, 1, -288, 780, -728, 269, -34, 1, 34560, -93888, 88140, -33008, 4349, -154, 1, -24883200, 67633920, -63554688, 23853900, -3164288, 115229, -874, 1, 125411328000, -340899840000, 320383261440, -120287210688, 15971865420, -583918448, 4520189 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS These are inspired by Cornelius-Schultz matrices. Row sums are: {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...} LINKS E. F. Cornelius and Phill Schultz, Sequences Generated by Polynomials, Amer. Math. Monthly, No. 2, 2008. FORMULA p(x,0)=1; p(x,1)=x-1; p(x,n)=(x-Gamma(n))*p(x,n-1) EXAMPLE Triangle begins: {1}, {-1, 1}, {1, -2, 1}, {-2, 5, -4, 1}, {12, -32, 29, -10, 1}, {-288, 780, -728, 269, -34, 1}, {34560, -93888, 88140, -33008, 4349, -154, 1} MATHEMATICA 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}]; CROSSREFS Sequence in context: A104560 A121435 A137156 * A209133 A078016 A078046 Adjacent sequences:  A136454 A136455 A136456 * A136458 A136459 A136460 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Mar 20 2008 EXTENSIONS Edited by N. J. A. Sloane, Aug 10 2008 STATUS approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)