A159508 - OEIS

%I #12 Sep 08 2022 08:45:43

%S 1,3,-89,-855,23601,405963,-10346601,-269746047,6288530145,

%T 230346491283,-4855444114041,-240305893799463,4513251073537809,

%U 296139484328781915,-4861463414700822921,-420887762743191256143,5883687931380635925441,677603075775465797408547

%N Numerator of Hermite(n, 3/14).

%H G. C. Greubel, <a href="/A159508/b159508.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 02 2018: (Start)

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

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

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

%t Numerator[Table[HermiteH[n,3/14],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 14 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,3/14)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (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

%Y Cf. A159507.

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009