A143507 Triangle of coefficients of x^n*H_n(x + 1/x), where H_n(x) is the Hermite polynomial of order n.

1, 2, 0, 2, 4, 0, 6, 0, 4, 8, 0, 12, 0, 12, 0, 8, 16, 0, 16, 0, 12, 0, 16, 0, 16, 32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32, 64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64, 128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128, 256, 0, -1536, 0, -896, 0, 896, 0, 1680, 0, 896, 0, -896, 0, -1536, 0, 256, 512, 0, -4608, 0, 512

Offset

0,2

Comments

Row sums yield A144141.

Links

Table of n, a(n) for n=0..85.

Wikipedia, Hermite polynomials

Formula

E.g.f.: exp(2*(1 + x^2)*y - x^2*y^2). - Franck Maminirina Ramaharo, Oct 25 2018

Example

Triangle begins:
     1;
     2, 0,    2;
     4, 0,    6, 0,    4;
     8, 0,   12, 0,   12, 0,    8;
    16, 0,   16, 0,   12, 0,   16, 0,   16;
    32, 0,    0, 0,  -40, 0,  -40, 0,    0, 0,   32;
    64, 0,  -96, 0, -240, 0, -280, 0, -240, 0,  -96, 0,   64;
   128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128;
    ... reformatted. - Franck Maminirina Ramaharo, Oct 25 2018

Mathematica

Table[CoefficientList[FullSimplify[x^n*HermiteH[n, x + 1/x]], x], {n,
  0, 10}]//Flatten

Prog

(PARI) row(n) = Vec(x^n*subst(polhermite(n, x), x, x+1/x));
for (n=0, 10, print(row(n))); \\ Michel Marcus, Oct 27 2018

Crossrefs

Cf. A060821.

Cf. A143505, A143506.

Sequence in context: A137312 A137320 A263399 * A172040 A317327 A120557

Adjacent sequences: A143504 A143505 A143506 * A143508 A143509 A143510

Keyword

sign,tabf

Author

Roger L. Bagula and Gary W. Adamson, Oct 25 2008

Extensions

Edited, new name and offset corrected by Franck Maminirina Ramaharo, Oct 25 2018

Status

approved