A159509 Numerator of Hermite(n, 5/14).

1, 5, -73, -1345, 14737, 600925, -4216505, -374426425, 1020390305, 298652268725, 593277094615, -289712837877425, -2088116897382095, 330261712856941325, 4311569491549495655, -431561222581976019625, -8495813265487638710975, 634208930681100205217125

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.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(5/7)^(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,5/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,5/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 7^n * Hermite(n,5/14).

E.g.f.: exp(5*x-49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/7)^(n-2*k)/(k!*(n-2*k)!)). (End)