A159516 Numerator of Hermite(n, 7/15).

1, 14, -254, -16156, 116716, 30714824, 167396536, -80586473296, -1655509714544, 266934167861984, 10441892693970976, -1055017257663334336, -66457610442443011904, 4766686645187803247744, 455510634120920865106816, -23652976986990268349291776

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..412

Crossrefs

Cf. A159513, A159514, A159515.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(14/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018

Mathematica

Numerator[Table[HermiteH[n,7/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

PARI

a(n)=numerator(polhermite(n,7/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 11 2018: (Start)

a(n) = 15^n * Hermite(n,7/15).

E.g.f.: exp(14*x-225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/15)^(n-2*k)/(k!*(n-2*k)!)). (End)