A160063 - OEIS

%I #15 Sep 08 2022 08:45:44

%S 1,36,46,-88344,-3352884,321016176,32512107336,-1237185455904,

%T -329019615602544,527148397348416,3720448017833162976,

%U 127346773675138667136,-46571676392900998903104,-3586781955271515967551744,627665590994866657343577216,85364645493066729096524299776

%N Numerator of Hermite(n, 18/25).

%H G. C. Greubel, <a href="/A160063/b160063.txt">Table of n, a(n) for n = 0..380</a>

%F From _G. C. Greubel_, Sep 23 2018: (Start)

%F a(n) = 25^n * Hermite(n, 18/25).

%F E.g.f.: exp(36*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 36/25, 46/625, -88344/15625, -3352884/390625, ...

%t Numerator[HermiteH[Range[0,20],18/25]] (* _Harvey P. Dale_, Mar 18 2015 *)

%t Table[25^n*HermiteH[n, 18/25], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 18/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 625*x^2))) \\ _G. C. Greubel_, Sep 23 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018

%Y Cf. A009969 (denominators).

%K sign,frac

%O 0,2

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