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 A159969 Numerator of Hermite(n, 13/24). 1

%I #13 Sep 08 2022 08:45:44

%S 1,13,-119,-9035,-14639,10218013,153914329,-15655840187,-513817209695,

%T 29391432064813,1713902824372009,-62366587629825323,

%U -6240409786798253711,134413599620299018045,25111471036836549128569,-215506510190170502086043,-111283139511606108762536639

%N Numerator of Hermite(n, 13/24).

%H G. C. Greubel, <a href="/A159969/b159969.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, 13/24).

%F E.g.f.: exp(13*x - 144*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 13/12, -119/144, -9035/1728, -14639/20736, ...

%t Numerator[Table[HermiteH[n, 13/24], {n, 0, 30}]] (* or *) Table[12^n* HermiteH[n, 1/12], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 13/24)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 144*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/12)^(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 May 18 12:17 EDT 2024. Contains 372630 sequences. (Running on oeis4.)