A158727 a(n) = Hermite(n, 21).

1, 42, 1762, 73836, 3090540, 129211992, 5395998264, 225081383184, 9377874118032, 390269410826400, 16222513520584224, 673540179648009408, 27931792247763542208, 1156970310094516546944, 47866526425527842874240

Offset

0,2

Comments

The first negative term is a(235). - Georg Fischer, Feb 16 2019

Links

G. C. Greubel, Table of n, a(n) for n = 0..670

Formula

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

E.g.f.: exp(42*x - x^2).

a(n) = 42*a(n-1) - 2*(n-1)*a(n-2). (End)

Mathematica

Table[HermiteH[n, 21], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[42*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(42*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(42*x - x^2))) \\ G. C. Greubel, Jul 13 2018
(PARI) for(n=0, 30, print1(polhermite(n, 21), ", ")) \\ G. C. Greubel, Jul 13 2018

Crossrefs

Sequence in context: A170723 A170761 A218744 * A208779 A208500 A207588

Adjacent sequences: A158724 A158725 A158726 * A158728 A158729 A158730

Keyword

sign

Author

N. J. A. Sloane, Nov 11 2009

Status

approved