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 A160059 Numerator of Hermite(n, 13/25). 1

%I

%S 1,26,-574,-79924,74476,401556376,9974990776,-2752323059824,

%T -158841568845424,23393349808258976,2395194744525753376,

%U -230141809245567612224,-38917614777613866837824,2440269154465553645576576,695858238152329730899630976,-24612396011186615794199674624

%N Numerator of Hermite(n, 13/25).

%H G. C. Greubel, <a href="/A160059/b160059.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, 13/25).

%F E.g.f.: exp(26*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 26/25, -574/625, -79924/15625, 74476/390625

%p seq(coeff(series(factorial(n)*exp(26*x-625*x^2), x,n+1),x,n),n=0..15); # _Muniru A Asiru_, Jul 17 2018

%t Numerator[HermiteH[Range[0,20],13/25]] (* _Harvey P. Dale_, Sep 24 2012 *)

%t Table[25^n*HermiteH[n, 13/25], {n, 0, 30}] (* _G. C. Greubel_, Jul 17 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 13/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 625*x^2))) \\ _G. C. Greubel_, Jul 17 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(26/25)^(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)*(26/25)^(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 April 16 10:22 EDT 2021. Contains 343036 sequences. (Running on oeis4.)