A159869 - OEIS

%I #16 Sep 08 2022 08:45:44

%S 1,10,-958,-30740,2733292,157424600,-12884868680,-1128180047600,

%T 84143536968080,10390351292567200,-697311246084385760,

%U -116903029136204833600,6946277990568033138880,1553663637818936898774400,-80002471104083358804411520,-23812890514414926932690528000

%N Numerator of Hermite(n, 5/23).

%H Robert Israel, <a href="/A159869/b159869.txt">Table of n, a(n) for n = 0..385</a>

%F a(n) = 10*a(n-1) + 1058*(1-n)*a(n-2). - _Robert Israel_, Dec 07 2017

%F From _G. C. Greubel_, Jul 11 2018: (Start)

%F a(n) = 23^n * Hermite(n, 5/23).

%F E.g.f.: exp(10*x - 529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 10/23, -958/529, -30740/12167, 2733292/279841

%p f:= gfun:-rectoproc({a(n) = -(1058*n-1058)*a(n-2)+10*a(n-1), a(0) = 1, a(1) = 10},a(n),remember):

%p map(f, [$0..40]); # _Robert Israel_, Dec 07 2017

%t Numerator[Table[HermiteH[n, 5/23], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)

%t Table[23^n*HermiteH[n, 5/23], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 5/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018

%Y Cf. A009967 (denominators)

%K sign,frac

%O 0,2

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