A158700 a(n) = Hermite(n, 18).

1, 36, 1294, 46440, 1664076, 59535216, 2126627016, 75844149984, 2700616621200, 96008691963456, 3407701811502816, 120757091374832256, 4272285849640899264, 150904120394076399360, 5321468902096086996096, 187347565104424992677376

Offset

0,2

Comments

The first negative term is a(175). - Georg Fischer, Feb 15 2019

Links

G. C. Greubel, Table of n, a(n) for n = 0..685

Formula

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

E.g.f.: exp(36*x - x^2).

a(n) = 36*a(n-1) - 2*(n-1)*a(n-2). (End)

Mathematica

Table[HermiteH[n, 18], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[36*x - x^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 13 2018 *)
nxt[{n_, a_, b_}]:={n+1, b, 36b-2a*n}; NestList[nxt, {1, 1, 36}, 20][[;; , 2]] (* Harvey P. Dale, Jun 09 2024 *)

Prog

(PARI) a(n)=polhermite(n, 18) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - x^2))) \\ G. C. Greubel, Jul 13 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(36*x - x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 13 2018

Crossrefs

Sequence in context: A170717 A170755 A218738 * A144128 A223405 A224267

Adjacent sequences: A158697 A158698 A158699 * A158701 A158702 A158703

Keyword

sign

Author

N. J. A. Sloane, Nov 11 2009

Status

approved