A054373 Table of resultants for Hermite polynomials H_k(x) and H_n(x).

0, -8, 0, 0, -2048, 0, 192, 16384, 28311552, 0, 0, -1179648, 0, 29686813949952, 0, -7680, 67108864, -289910292480, 5699868278390784, -3039929748475084800000, 0, 0, -838860800, 0, 1094374709451030528, 0, -37180135792929290696471347200000, 0

Offset: 1

Author

Eric W. Weisstein

Keywords

• sign
• easy
• tabl

Examples

			{0},
{-8, 0},
{0, -2048, 0},
{192, 16384, 28311552, 0},
{0, -1179648, 0, 29686813949952, 0},
{-7680, 67108864, -289910292480, 5699868278390784, -3039929748475084800000, 0}
		

Links

• G. C. Greubel, Rows n=1..30 of triangle, flattened
• Eric Weisstein's World of Mathematics, Hermite Polynomial.
• Index entries for sequences related to Hermite polynomials

Programs

Mathematica

Flatten[Table[Resultant[HermiteH[n, x], HermiteH[k, x], x], {k, 20}, {n, k}]]

PARI

T(n, k) = polresultant(polhermite(n), polhermite(k)); \\ Michel Marcus, Jul 10 2018