A160147 Numerator of Hermite(n, 19/27).

1, 38, -14, -111340, -4169684, 490886888, 49050698104, -2430351968272, -592964799643760, 5814962971461728, 8001852693840964384, 219288242242044652352, -120000760298623690001216, -8396695977614513457596800, 1955419963550761908894369664

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 38/27, -14/729, -111340/19683, -4169684/531441, ...
		

Links

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

Crossrefs

Cf. A009971 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(38/27)^(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

Table[27^n*HermiteH[n, 19/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PARI

a(n)=numerator(polhermite(n, 19/27)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(38*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, 19/27).

E.g.f.: exp(38*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/27)^(n-2*k)/(k!*(n-2*k)!)). (End)