A159517 Numerator of Hermite(n, 8/15).

1, 16, -194, -17504, -18164, 31216576, 540334216, -75639407744, -2912283304304, 225705335009536, 15406032742583776, -769177483661571584, -88566701814374836544, 2736491182742489168896, 561899064537972620484736, -8249509418670119836289024

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. A159515, A159516.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(16/15)^(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,8/15],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)

PARI

a(n)=numerator(polhermite(n,8/15)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 15^n * Hermite(n,8/15).

E.g.f.: exp(16*x-225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/15)^(n-2*k)/(k!*(n-2*k)!)). (End)