A160148 Numerator of Hermite(n, 20/27).

1, 40, 142, -110960, -5059508, 444738400, 54673349320, -1703637550400, -626141705175920, -5174439819171200, 8009253862551574240, 395813487065579065600, -112619873964978985037120, -11429947728298530733222400, 1677399182000270453064676480

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 40/27, 142/729, -110960/19683, -5059508/531441, ...
		

Links

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

Crossrefs

Cf. A009971 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(40/27)^(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, 20/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PARI

a(n)=numerator(polhermite(n, 20/27)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(40*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, 20/27).

E.g.f.: exp(40*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/27)^(n-2*k)/(k!*(n-2*k)!)). (End)