A176064 A symmetrical triangle of polynomial coefficients based on the Hermite polynomials with leading coefficient adjusted to one: p(x,n)=HermiteH[n,x]-HermiteH[0,x]+x^n*(HermiteH[n,1/x]-HermiteH[0,1/x])

1, 1, 1, 1, 0, 1, 1, -18, -18, 1, 1, -26, -122, -26, 1, 1, 90, -190, -190, 90, 1, 1, 58, 298, 58, 298, 58, 1, 1, -1806, -1470, 3234, 3234, -1470, -1806, 1, 1, -1934, -18958, -1934, 24946, -1934, -18958, -1934, 1, 1, 29730, -9726, -81150, 47874, 47874, -81150

Offset

0,8

Comments

Row sums are:

{1, 2, 2, -34, -172, -198, 772, -82, -20704, -26542, 337844,...}.

Links

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

Formula

p(x,n)=HermiteH[n,x]-HermiteH[0,x]+x^n*(HermiteH[n,1/x]-HermiteH[0,1/x]);

t(n,m)=Coefficients(p(x,n));

out_n,m=t(n,m)-t(n,0)+1

Example

{1},
{1, 1},
{1, 0, 1},
{1, -18, -18, 1},
{1, -26, -122, -26, 1},
{1, 90, -190, -190, 90, 1},
{1, 58, 298, 58, 298, 58, 1},
{1, -1806, -1470, 3234, 3234, -1470, -1806, 1},
{1, -1934, -18958, -1934, 24946, -1934, -18958, -1934, 1},
{1, 29730, -9726, -81150, 47874, 47874, -81150, -9726, 29730, 1},
{1, 29218, 308578, 29218, -212702, 29218, -212702, 29218, 308578, 29218, 1}

Mathematica

a = Table[CoefficientList[HermiteH[n, x] - HermiteH[ 0, x], x] + Reverse[CoefficientList[HermiteH[n, x] - HermiteH[0, x], x]], {n, 0, 10}];
Table[Table[a[[n]][[m]] - a[[n]][[1]] + 1, {m, 1, n}], {n, 1, Length[a]}];
Flatten[%]

Crossrefs

Sequence in context: A029926 A070742 A304260 * A278716 A282814 A010857

Adjacent sequences: A176061 A176062 A176063 * A176065 A176066 A176067

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 07 2010

Status

approved