A176411 A symmetrical triangle of leading ones adjusted polynomial coefficients based on Hermite orthogonal polynomials: 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

1, 1, 1, 1, -1, 1, 1, -19, -19, 1, 1, -27, -123, -27, 1, 1, 89, -191, -191, 89, 1, 1, 57, 297, 57, 297, 57, 1, 1, -1807, -1471, 3233, 3233, -1471, -1807, 1, 1, -1935, -18959, -1935, 24945, -1935, -18959, -1935, 1, 1, 29729, -9727, -81151, 47873, 47873, -81151

Offset

0,8

Comments

Row sums are:

{1, 2, 1, -36, -175, -202, 767, -88, -20711, -26550, 337835,...}.

Sequence A176410 was discovered by a typing mistake;

I left out the plus signs and Mathematica made it multiplication instead.

Links

Table of n, a(n) for n=0..51.

Formula

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

Example

{1},
{1, 1},
{1, -1, 1},
{1, -19, -19, 1},
{1, -27, -123, -27, 1},
{1, 89, -191, -191, 89, 1},
{1, 57, 297, 57, 297, 57, 1},
{1, -1807, -1471, 3233, 3233, -1471, -1807, 1},
{1, -1935, -18959, -1935, 24945, -1935, -18959, -1935, 1},
{1, 29729, -9727, -81151, 47873, 47873, -81151, -9727, 29729, 1},
{1, 29217, 308577, 29217, -212703, 29217, -212703, 29217, 308577, 29217, 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[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A305238 A004460 A082126 * A131382 A291475 A057430

Adjacent sequences: A176408 A176409 A176410 * A176412 A176413 A176414

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 16 2010

Status

approved