A160038 - OEIS

%I #12 Sep 08 2022 08:45:44

%S 1,24,-674,-76176,699276,397662624,5173427976,-2858307408576,

%T -113866872595824,25850269143460224,1901408776146065376,

%U -277494553665747230976,-32804239959986332463424,3375116545946536485517824,614071696452494778183067776,-44326818839204513820168293376

%N Numerator of Hermite(n, 12/25).

%H G. C. Greubel, <a href="/A160038/b160038.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, 12/25).

%F E.g.f.: exp(24*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 24/25, -674/625, -76176/15625, 699276/390625

%p seq(coeff(series(factorial(n)*exp(24*x-625*x^2), x,n+1),x,n),n=0..15); # _Muniru A Asiru_, Jul 17 2018

%t Numerator[Table[HermiteH[n, 12/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 12/25], {n, 0, 30}] (* _G. C. Greubel_, Jul 17 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 12/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 625*x^2))) \\ _G. C. Greubel_, Jul 17 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/25)^(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)*(24/25)^(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