A160012 - OEIS

%I #14 Sep 08 2022 08:45:44

%S 1,16,-994,-55904,2833036,324848576,-12508897784,-2636506684544,

%T 67268748657296,27441366823956736,-317711553211272224,

%U -348100470150839555584,-1201073665758439809344,5202289873610458296810496,102754085046341979650807936,-89396007427441548519770753024

%N Numerator of Hermite(n, 8/25).

%H G. C. Greubel, <a href="/A160012/b160012.txt">Table of n, a(n) for n = 0..380</a>

%F From _G. C. Greubel_, Jul 17 2018: (Start)

%F a(n) = 25^n * Hermite(n, 8/25).

%F E.g.f.: exp(16*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 16/25, -994/625, -55904/15625, 2833036/390625

%p seq(coeff(series(factorial(n)*exp(16*x-625*x^2), x,n+1),x,n),n=0..15); # _Muniru A Asiru_, Jul 17 2018

%t Numerator[HermiteH[Range[0,20],8/25]] (* _Harvey P. Dale_, Sep 29 2013 *)

%t Table[25^n*HermiteH[n, 8/25], {n, 0, 30}] (* _G. C. Greubel_, Jul 17 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 8/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 625*x^2))) \\ _G. C. Greubel_, Jul 17 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 17 2018

%o (GAP) List(List([0..15],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(16/25)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # _Muniru A Asiru_, Jul 17 2018

%Y Cf. A009969 (denominators).

%K sign,frac

%O 0,2

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