The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 23:32 EST 2022. Contains 358671 sequences. (Running on oeis4.)