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A160069 Numerator of Hermite(n, 1/26). 1

%I

%S 1,1,-337,-1013,340705,1710281,-574081169,-4042531037,1354233514817,

%T 12285237438865,-4107293114634449,-45631395657998149,

%U 15225284404552883233,200306225193393375577,-66699593448411975550225,-1014548651063549428780589,337152390132385166610860161

%N Numerator of Hermite(n, 1/26).

%H G. C. Greubel, <a href="/A160069/b160069.txt">Table of n, a(n) for n = 0..422</a>

%F From _G. C. Greubel_, Sep 23 2018: (Start)

%F a(n) = 13^n * Hermite(n, 1/26).

%F E.g.f.: exp(x - 169*x^2).

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

%e Numerators of 1, 1/13, -337/169, -1013/2197, 340705/28561, ...

%t Table[13^n*HermiteH[n, 1/26], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 1/26)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 169*x^2))) \\ _G. C. Greubel_, Sep 23 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(1/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018

%Y Cf. A001022 (denominators).

%K sign,frac

%O 0,3

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

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Last modified August 3 02:27 EDT 2021. Contains 346430 sequences. (Running on oeis4.)