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A160220 Numerator of Hermite(n, 19/28). 1

%I #13 Sep 08 2022 08:45:45

%S 1,19,-31,-15485,-257759,19383059,873485761,-28992725309,

%T -2947706709055,34914759096979,11062889692388641,73329048495226499,

%U -46309928432170516511,-1224828484332785265005,212723654088018032104961,10763608149690668144341699,-1046306531193423334034678399

%N Numerator of Hermite(n, 19/28).

%H G. C. Greubel, <a href="/A160220/b160220.txt">Table of n, a(n) for n = 0..417</a>

%F From _G. C. Greubel_, Sep 26 2018: (Start)

%F a(n) = 14^n * Hermite(n, 19/28).

%F E.g.f.: exp(19*x - 196*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 19/14, -31/196, -15485/2744, -257759/38416

%t Numerator[HermiteH[Range[0,20],19/28]] (* _Harvey P. Dale_, Jul 26 2015 *)

%t Table[14^n*HermiteH[n, 19/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 19/28)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 196*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018

%Y Cf. A001023 (denominators).

%K sign,frac

%O 0,2

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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)