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%I A160300 #17 Sep 08 2022 08:45:45
%S A160300 1,4,-1906,-23000,10897996,220415984,-103848077624,-2957229437984,
%T A160300 1385343118601360,51011732312847424,-23759618336314935584,
%U A160300 -1075483968398187231616,498023914992777619190464,26797057907106900786753280,-12336437308381113989945920384
%N A160300 Numerator of Hermite(n, 2/31).
%H A160300 G. C. Greubel, <a href="/A160300/b160300.txt">Table of n, a(n) for n = 0..368</a>
%F A160300 a(n+2) = 4*a(n+1) - 1922*(n+1)*a(n). - _Bruno Berselli_, Mar 28 2018
%F A160300 From _G. C. Greubel_, Oct 04 2018: (Start)
%F A160300 a(n) = 31^n * Hermite(n, 2/31).
%F A160300 E.g.f.: exp(4*x - 961*x^2).
%F A160300 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160300 Numerators of 1, 4/31, -1906/961, -23000/29791, 10897996/923521, ...
%t A160300 Table[31^n*HermiteH[n, 2/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o A160300 (PARI) a(n)=numerator(polhermite(n, 2/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160300 (PARI) x='x+O('x^30); Vec(serlaplace(exp(4*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o A160300 (Maxima) makelist(num(hermite(n, 2/31)), n, 0, 20); /* _Bruno Berselli_, Mar 28 2018 */
%o A160300 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018
%Y A160300 Cf. A009975 (denominators).
%K A160300 sign,frac
%O A160300 0,2
%A A160300 _N. J. A. Sloane_, Nov 12 2009

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