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A160060 Numerator of Hermite(n, 14/25). 1

%I

%S 1,28,-466,-83048,-577844,399060368,14785215304,-2578966731488,

%T -201581702391664,20145379647913408,2831864782047795424,

%U -172525031701579328128,-43768841640801408267584,1362347909581250490427648,749389418131297898080214144,-2858184709995542436237843968

%N Numerator of Hermite(n, 14/25).

%H G. C. Greubel, <a href="/A160060/b160060.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, 14/25).

%F E.g.f.: exp(28*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 28/25, -466/625, -83048/15625, -577844/390625...

%p seq(coeff(series(factorial(n)*exp(28*x-625*x^2), x,n+1),x,n),n=0..15); # _Muniru A Asiru_, Jul 17 2018

%t Numerator[HermiteH[Range[0,20],14/25]] (* _Harvey P. Dale_, Aug 21 2011 *)

%t Table[25^n*HermiteH[n, 14/25], {n, 0, 30}] (* _G. C. Greubel_, Jul 17 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 14/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 625*x^2))) \\ _G. C. Greubel_, Jul 17 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(28/25)^(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)*(28/25)^(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

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Last modified March 2 09:23 EST 2021. Contains 341746 sequences. (Running on oeis4.)