A159197 Numerator of Hermite(n, 2/9).

1, 4, -146, -1880, 63436, 1471984, -45495224, -1612749344, 45140586640, 2270685496384, -56732233335584, -3905439437484416, 85475082054073024, 7934074594685996800, -148274224427133801344, -18587578078456375947776, 285956053044109633474816

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A159030.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(4/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018

Mathematica

Numerator[Table[HermiteH[n,2/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)

PARI

a(n)=numerator(polhermite(n,2/9)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 10 2018: (Start)

a(n) = 9^n * Hermite(n,2/9).

E.g.f.: exp(4*x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/9)^(n-2*k)/(k!*(n-2*k)!)). (End)