A160142 Numerator of Hermite(n, 16/27).

1, 32, -434, -107200, -1532084, 576163712, 29606131144, -4092883955968, -433132461046640, 33879159708918272, 6767697264539394784, -277391836090767772672, -117416867483587382271296, 1095907804769276717987840, 2260588356036532098545755264

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 32/27, -434/729, -107200/19683, -1532084/531441, ...
		

Links

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

Crossrefs

Cf. A009971 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(32/27)^(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, 16/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PARI

a(n)=numerator(polhermite(n, 16/27)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(32*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, 16/27).

E.g.f.: exp(32*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/27)^(n-2*k)/(k!*(n-2*k)!)). (End)