A158703 a(n) = Hermite(n, 20).

1, 40, 1598, 63760, 2540812, 101122400, 4019487880, 159566046400, 6326369025680, 250501704284800, 9906193528929760, 391237707071494400, 15431572025223321280, 607873176039216985600, 23913706168912873070720

Offset

0,2

Comments

The first negative term is a(214). - Georg Fischer, Feb 16 2019

Links

G. C. Greubel, Table of n, a(n) for n = 0..675

Formula

From G. C. Greubel, Jul 13 2018: (Start)

E.g.f.: exp(40*x - x^2).

a(n) = 40*a(n-1) - 2*(n-1)*a(n-2). (End)

Mathematica

Table[HermiteH[n, 20], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[40*x - x^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 13 2018 *)

Prog

(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(40*x - x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 13 2018
(PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - x^2))) \\ G. C. Greubel, Jul 13 2018
(PARI) for(n=0, 30, print1(polhermite(n, 20), ", ")) \\ G. C. Greubel, Jul 13 2018

Crossrefs

Sequence in context: A063820 A170759 A218742 * A209223 A207692 A207927

Adjacent sequences: A158700 A158701 A158702 * A158704 A158705 A158706

Keyword

sign

Author

N. J. A. Sloane, Nov 11 2009

Status

approved