%I #19 Sep 08 2022 08:45:45

%S 1,2,-1918,-11524,11036140,110668792,-105835967816,-1487904444976,

%T 1420941302106512,25719901350164000,-24528002841138116576,

%U -543392509632428313152,517484251048077204023488,13567773344258481022584704,-12902725949998740057685701760

%N Numerator of Hermite(n, 1/31).

%H G. C. Greubel, <a href="/A160299/b160299.txt">Table of n, a(n) for n = 0..368</a>

%F a(n+2) = 2*a(n+1) - 1922*(n+1)*a(n). - _Bruno Berselli_, Mar 28 2018

%F From _G. C. Greubel_, Oct 04 2018: (Start)

%F a(n) = 31^n * Hermite(n, 1/31).

%F E.g.f.: exp(2*x - 961*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 2/31, -1918/961, -11524/29791, 11036140/923521, ...

%t Table[31^n*HermiteH[n, 1/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 1/31)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(2*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018

%o (Maxima) makelist(num(hermite(n, 1/31)), n, 0, 20); /* _Bruno Berselli_, Mar 28 2018 */

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/31)^(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 Cf. A009975 (denominators).

%K sign,frac

%O 0,2

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