A160252 - OEIS

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

%S 1,18,-1358,-84996,5322540,667658808,-32744702856,-7327417341744,

%T 253642619275152,103163294897460000,-1982702662432970976,

%U -1770895268099070677568,4807849834551556801728,35830291388333570578463616,539816800507699929385760640

%N Numerator of Hermite(n, 9/29).

%H G. C. Greubel, <a href="/A160252/b160252.txt">Table of n, a(n) for n = 0..371</a>

%F From _G. C. Greubel_, Sep 26 2018: (Start)

%F a(n) = 29^n * Hermite(n, 9/29).

%F E.g.f.: exp(18*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 18/29, -1358/841, -84996/24389, 5322540/707281,...

%t Table[29^n*HermiteH[n, 9/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%t HermiteH[Range[0,20],9/29]//Numerator (* _Harvey P. Dale_, Feb 17 2021 *)

%o (PARI) a(n)=numerator(polhermite(n, 9/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018

%Y Cf. A009973 (denominators).

%K sign,frac

%O 0,2

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