A158980 - OEIS

%I #18 Sep 08 2022 08:45:43

%S 1,2,-94,-580,26476,280312,-12412616,-189648688,8135757200,

%T 164956085792,-6845825678816,-175348615433792,7029102850896064,

%U 220268177451931520,-8514540677137722496,-319237020818325490432,11877900753755801088256,524319450150645971173888

%N Numerator of Hermite(n, 1/7).

%H G. C. Greubel, <a href="/A158980/b158980.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 09 2018: (Start)

%F a(n) = 7^n * Hermite(n,1/7).

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

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

%t Numerator[Table[HermiteH[n,1/7],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)

%o (PARI) a(n)=numerator(polhermite(n,1/7)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y Cf. A158811, A158954, A158960.

%K sign,frac

%O 0,2

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