A159508 Numerator of Hermite(n, 3/14).

1, 3, -89, -855, 23601, 405963, -10346601, -269746047, 6288530145, 230346491283, -4855444114041, -240305893799463, 4513251073537809, 296139484328781915, -4861463414700822921, -420887762743191256143, 5883687931380635925441, 677603075775465797408547

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)*(3/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 10 2018

Mathematica

Numerator[Table[HermiteH[n,3/14],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *)

PARI

a(n)=numerator(polhermite(n,3/14)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 02 2018: (Start)

a(n) = 7^n * Hermite(n,3/14).

E.g.f.: exp(3*x-49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/7)^(n-2*k)/(k!*(n-2*k)!)). (End)