A160087 Numerator of Hermite(n, 1/27).

1, 2, -1454, -8740, 6342316, 63656312, -46108171016, -649081759408, 469281829870480, 8509453301475872, -6140897264957486816, -136349623665433187392, 98215011088057307180224, 2582003037826533660970880, -1856403314087385132972023936

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 2/27, -1454/729, -8740/19683, 6342316/531441..
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..376

Crossrefs

Cf. A009971 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(2/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Mathematica

Table[27^n*HermiteH[n, 1/27], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

PARI

a(n)=numerator(polhermite(n, 1/27)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(2*x - 729*x^2))) \\ G. C. Greubel, Sep 23 2018

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 27^n * Hermite(n, 1/27).

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

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