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A159968 Numerator of Hermite(n, 11/24). 1

%I #15 Sep 08 2022 08:45:44

%S 1,11,-167,-8173,54385,10013531,31834441,-16953202717,-250663462943,

%T 36302880967595,1049051386591801,-93012731934163789,

%U -4346534843998627247,273640118280485155067,19283467757016197118505,-891198811579737976926589,-93107767637687089298134079

%N Numerator of Hermite(n, 11/24).

%H G. C. Greubel, <a href="/A159968/b159968.txt">Table of n, a(n) for n = 0..428</a>

%F From _G. C. Greubel_, Jul 16 2018: (Start)

%F a(n) = 12^n * Hermite(n, 11/24).

%F E.g.f.: exp(11*x - 144*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 11/12, -167/144, -8173/1728, 54385/20736, ...

%t Numerator[HermiteH[Range[0,20],11/24]] (* _Harvey P. Dale_, Mar 27 2013 *)

%t Table[12^n*HermiteH[n, 11/12], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 11/24)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(11*x - 144*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018

%Y Cf. A001021 (denominators).

%K sign,frac

%O 0,2

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

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Last modified June 12 10:55 EDT 2024. Contains 373331 sequences. (Running on oeis4.)