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

%S 1,29,391,-14761,-955919,-1151851,2117414071,64515005759,

%T -4798919156639,-371422676274931,8664364972414951,1922668627437223079,

%U 12868783582225461841,-10009215864276466233211,-365549644020036472532969,52457120268360679565773199

%N Numerator of Hermite(n, 29/30).

%H G. C. Greubel, <a href="/A160298/b160298.txt">Table of n, a(n) for n = 0..412</a>

%F From _G. C. Greubel_, Oct 04 2018: (Start)

%F a(n) = 15^n * Hermite(n, 29/30).

%F E.g.f.: exp(29*x - 225*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(29/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 29/15, 391/225, -14761/3375, -955919/50625, ...

%t Table[15^n*HermiteH[n, 29/30], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 29/30)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(29*x - 225*x^2))) \\ _G. C. Greubel_, Oct 04 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(29/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018

%Y Cf. A001024 (denominators).

%K sign,frac

%O 0,2

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