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A160013 Numerator of Hermite(n, 9/25). 1

%I

%S 1,18,-926,-61668,2362476,350864568,-8449912776,-2783582689968,

%T 23832248370576,28264807370350368,240653738497326624,

%U -348978324836427720768,-9590598751393940053824,5062044095021324890551168,246964023420535373904561024,-84140419241303548854363341568

%N Numerator of Hermite(n, 9/25).

%H G. C. Greubel, <a href="/A160013/b160013.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, 9/25).

%F E.g.f.: exp(18*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 18/25, -926/625, -61668/15625, 2362476/390625

%p seq(coeff(series(factorial(n)*exp(18*x-625*x^2), x,n+1),x,n),n=0..15); # _Muniru A Asiru_, Jul 17 2018

%t Numerator[HermiteH[Range[0,20],9/25]] (* _Harvey P. Dale_, Oct 10 2012 *)

%t Table[25^n*HermiteH[n, 9/25], {n, 0, 30}] (* _G. C. Greubel_, Jul 17 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 9/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 625*x^2))) \\ _G. C. Greubel_, Jul 17 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(18/25)^(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)*(18/25)^(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 June 17 05:41 EDT 2021. Contains 345080 sequences. (Running on oeis4.)