A159242 Numerator of Hermite(n, 7/9).

1, 14, 34, -4060, -73364, 1603784, 81877816, -412588624, -98625684080, -846044720416, 131951621302816, 3217915145313344, -190086977127231296, -8916844722270378880, 275487347718163805056, 24080226698163512570624, -332311081180848870297344

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, A159197.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(14/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018

Mathematica

Numerator[Table[HermiteH[n,7/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

PARI

a(n)=numerator(polhermite(n,7/9)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 28 2018: (Start)

a(n) = 9^n * Hermite(n, 7/9).

E.g.f.: exp(14*x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/9)^(n-2*k)/(k!*(n-2*k)!)). (End)