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A159946 Numerator of Hermite(n, 20/23). 1

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

%S 1,40,542,-62960,-4238708,96898400,26298701320,436837009600,

%T -177294701591920,-10789176512931200,1256633088041014240,

%U 164414811028452665600,-8048103437483217101120,-2409334578316563726502400,14320231546481618948708480,36259873035884206674901888000

%N Numerator of Hermite(n, 20/23).

%H G. C. Greubel, <a href="/A159946/b159946.txt">Table of n, a(n) for n = 0..385</a>

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

%F a(n) = 23^n * Hermite(n, 20/23).

%F E.g.f.: exp(40*x - 529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 40/23, 542/529, -62960/12167, -4238708/279841, ...

%t Numerator[Table[HermiteH[n, 20/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 20/23], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 20/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/23)^(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. A009967 (denominators).

%K sign,frac

%O 0,2

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

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)