A176410 A symmetrical triangle of adjusted polynomial coefficients based on Hermite orthogonal polynomials.

1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, -191, 2113, -191, 1, 1, 1, 1, 1, 1, 1, 1, 7681, -337919, 7681, -337919, 7681, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -430079, 47738881, -430079, 180203521, -430079, 47738881, -430079, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,5

Comments

Row sums are: {1, 2, 11, 4, 1733, 6, -652793, 8, 273960969, 10, -143712092149, ...}.

Links

G. C. Greubel, Rows n = 0..50 of triangle, flattened

Example

Triangle begins as:
  1;
  1,    1;
  1,    9,       1;
  1,    1,       1,    1;
  1, -191,    2113, -191,       1;
  1,    1,       1,    1,       1,    1;
  1, 7681, -337919, 7681, -337919, 7681, 1;
  1,    1,       1,    1,       1,    1, 1, 1;

Mathematica

T[n_, m_]:= CoefficientList[HermiteH[n, x], x][[m + 1]]Reverse[ CoefficientList[ HermiteH[n, x], x]][[m + 1]] - (CoefficientList[ HermiteH[n, x], x][[1]]Reverse[CoefficientList[HermiteH[n, x], x]][[1]]) + 1;
Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten

Crossrefs

Cf. A060821.

Sequence in context: A113061 A366904 A284099 * A087966 A087968 A340365

Adjacent sequences: A176407 A176408 A176409 * A176411 A176412 A176413

Keyword

less,sign,tabl

Author

Roger L. Bagula, Apr 16 2010

Extensions

Edited by G. C. Greubel, Apr 26 2019

Status

approved