A160184 - OEIS

%I #13 Sep 08 2022 08:45:44

%S 1,1,-391,-1175,458641,2301041,-896635319,-6308683751,2454058631585,

%T 22238090874721,-8635680761357159,-95808996990263479,

%U 37141246445981806129,487826768288181211345,-188783965120435102822039,-2865977269485973590683399,1107183737638672431002905921

%N Numerator of Hermite(n, 1/28).

%H G. C. Greubel, <a href="/A160184/b160184.txt">Table of n, a(n) for n = 0..417</a>

%F From _G. C. Greubel_, Sep 24 2018: (Start)

%F a(n) = 14^n * Hermite(n, 1/28).

%F E.g.f.: exp(x - 196*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 1/14, -391/196, -1175/2744, 458641/38416, ...

%t Table[14^n*HermiteH[n, 1/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 1/28)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 196*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018

%Y Cf. A001023 (denominators).

%K sign,frac

%O 0,3

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