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A159947 Numerator of Hermite(n, 21/23). 1

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

%S 1,42,706,-59220,-4728084,52039512,27197223864,811936580112,

%T -167321303572080,-13899725964095328,1009444962121341984,

%U 189455789109224933568,-3790777326580730799936,-2564543346247110450176640,-55572469192587267485099136,35651972338523534753642227968

%N Numerator of Hermite(n, 21/23).

%H G. C. Greubel, <a href="/A159947/b159947.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, 21/23).

%F E.g.f.: exp(42*x - 529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 42/23, 706/529, -59220/12167, -4728084/279841, ...

%t Numerator[HermiteH[Range[0,20],21/23]] (* _Harvey P. Dale_, Dec 18 2015 *)

%t Table[23^n * HermiteH[n, 21/23], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 21/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(42*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(42/23)^(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 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)