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%I #21 Mar 18 2024 12:00:20
%S 1,34,274,-50660,-2447444,95515384,14040751096,-28081874864,
%T -87642381012080,-2781695245370336,601127582131299616,
%U 44972889856630550464,-4303061546712430158656,-622297158830800371505280,28180800294357511567970176,8642272527250878380658183424
%N Numerator of Hermite(n, 17/21).
%H G. C. Greubel, <a href="/A159776/b159776.txt">Table of n, a(n) for n = 0..390</a>
%F From _G. C. Greubel_, Jul 11 2018: (Start)
%F a(n) = 21^n * Hermite(n, 17/21).
%F E.g.f.: exp(34*x - 441*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(37/21)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n, 17/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%t Table[21^n*HermiteH[n, 17/21], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 17/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 21 2018
%Y Cf. A009965 (denominators)
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009