A160132 Numerator of Hermite(n, 10/27).

1, 20, -1058, -79480, 3038092, 524289200, -11661906680, -4819720055200, 22627018472080, 56669755093294400, 836483365475254240, -809515361950727267200, -29605827454506672845120, 13571164223599790810028800, 832572138044715293306980480

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 20/27, -1058/729, -79480/19683, 3038092/531441, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..375

Crossrefs

Cf. A009971 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(20/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Mathematica

Numerator/@(HermiteH[#,10/27]&/@Range[0,20])  (* Harvey P. Dale, Mar 30 2011 *)
Table[27^n*HermiteH[n, 10/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PARI

a(n)=numerator(polhermite(n, 10/27)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(20*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 27^n * Hermite(n, 10/27).

E.g.f.: exp(20*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/27)^(n-2*k)/(k!*(n-2*k)!)). (End)