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%I #15 Sep 08 2022 08:45:45
%S 1,52,782,-159224,-12788660,559103792,151972419784,1454980899424,
%T -1968977929003888,-124758638617745600,27571931007786483424,
%U 3831601446637967570048,-383682490141447518907712,-108323545252613355018788096,3953866345538313246451111040
%N Numerator of Hermite(n, 26/31).
%H Harvey P. Dale, <a href="/A160344/b160344.txt">Table of n, a(n) for n = 0..369</a>
%F From _G. C. Greubel_, Jul 12 2018: (Start)
%F a(n) = 31^n * Hermite(n, 26/31).
%F E.g.f.: exp(52*x - 961*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 52/31, 782/961, -159224/29791, -12788660/923521, ...
%t Numerator[HermiteH[Range[0,20],26/31]] (* _Harvey P. Dale_, Jan 26 2016 *)
%t Table[31^n*HermiteH[n, 26/31], {n,0,30}] (* _G. C. Greubel_, Jul 12 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,26/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(52/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 12 2018
%Y Cf. A009975 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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