A159510 Numerator of Hermite(n, 9/14).

1, 9, -17, -1917, -12255, 641169, 11775471, -271028133, -10517226303, 117831019545, 10336672775151, -22444344177741, -11344932349212447, -75709842389888607, 13772055231387660015, 227822400841416108939, -18194519582567115241599

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. A159507, A159508, A159509.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(9/7)^(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,9/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2011 *)
With[{nn=20},CoefficientList[Series[Exp[9x-49x^2],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Aug 11 2021 *)

PARI

a(n)=numerator(polhermite(n,9/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 7^n * Hermite(n,9/14).

E.g.f.: exp(9*x-49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/7)^(n-2*k)/(k!*(n-2*k)!)). (End)