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 A135049 Triangle read by rows: row n gives coefficients of increasing powers of x in the polynomial (-1)^n*p(n), where p(n) is defined as follows. Let f(n) = n*(n+1)/2, g(n) = f(n)+1; then p(-1) = 0, p(0) = 1 and for n >= 1, p(n) = (x - f(n))*p(n - 1) - g(n - 1)^2*p(n - 2). 1
 1, 1, -1, -1, -4, 1, -22, -7, 10, -1, -171, 148, 58, -20, 1, 97, 3238, -488, -237, 35, -1, 45813, 30013, -28334, 631, 716, -56, 1, 1235816, -772641, -587173, 160710, 2477, -1800, 84, -1, 5960643, -54291825, 3463307, 5842062, -673694, -20181, 3983, -120, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Inspired by the Cornelius-Schultz article. REFERENCES Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 256. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows E. F. Cornelius Jr. and P. Schultz, Sequences generated by polynomials, Amer. Math. Monthly, No. 2, 2008. EXAMPLE {1}, {1, -1}, {-1, -4, 1}, {-22, -7, 10, -1}, {-171, 148, 58, -20,1}, {97, 3238, -488, -237, 35, -1}, {45813, 30013, -28334, 631, 716, -56, 1}, {1235816, -772641, -587173, 160710, 2477, -1800, 84, -1}. MATHEMATICA a[n_] := n*(n + 1)/2; b[n_] = a[n] + 1; T[n_, m_, d_] := If[ n == m, a[n], If[n == m - 1 || n == m + 1, If[n == m - 1, b[m - 1], If[ n == m + 1, b[n - 1], 0]], 0]]; M0[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; TableForm[Table[M0[n], {n, 1, 4}]]; p1 = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[M0[n + 1], x], x], {n, 0, 10}]]; (* sequence values *) Flatten[p1] p[x, 0] = 1; p[x, -1] = 0; p[x_, j_] := p[x, j] = (x - a[j])*p[x, j - 1] - b[j - 1]^2*p[x, j - 2]; p2 = Join[{{1}}, Table[CoefficientList[(-1)^n*p[x, n], x], {n, 1, 11}]]; p1 - p2 CROSSREFS Sequence in context: A202550 A142472 A299445 * A113384 A243663 A039812 Adjacent sequences:  A135046 A135047 A135048 * A135050 A135051 A135052 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Feb 11 2008 EXTENSIONS Edited by N. J. A. Sloane, Mar 02 2008 STATUS approved

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Last modified May 21 10:48 EDT 2019. Contains 323443 sequences. (Running on oeis4.)