A197355 Special values of Hermite polynomials.

1, 8, 66, 560, 4876, 43488, 396664, 3695168, 35114640, 340039808, 3352381984, 33619852032, 342711219904, 3548566208000, 37299021381504, 397752024876032, 4300986840453376, 47135959519660032, 523321228732695040, 5883464372569321472, 66953921672396983296

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

In Maple notation, a(n)=I^n*HermiteH(n,-4*I), n=0,1... .

E.g.f.: exp(8*x+x^2).

Recurrence: a(n) = 8*a(n-1) + 2*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 2^(n/2-1/2)*exp(4*sqrt(2*n)-n/2-8)*n^(n/2)*(1+19/3*sqrt(2)/sqrt(n)). - Vaclav Kotesovec, Oct 20 2012

Mathematica

CoefficientList[Series[E^(8*x+x^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 20 2012 *)

Prog

(PARI) {a(n) = if( n<0, 0, n! * polcoeff( exp( 8*x + x^2 + x*O(x^n) ), n))} /* Michael Somos, Oct 29 2011 */

Crossrefs

Sequence in context: A162758 A004331 A147959 * A121777 A056621 A152275

Adjacent sequences: A197352 A197353 A197354 * A197356 A197357 A197358

Keyword

nonn

Author

Karol A. Penson, Oct 17 2011

Status

approved