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%I #17 Sep 08 2022 08:45:44
%S 1,21,199,-5985,-270159,120141,329415351,6743277639,-416420774175,
%T -21799821766779,449168189050791,62188100645671791,110264394305901969,
%U -178278691994606939715,-4090744316373113328489,518102577833892931856151,25729556002946152951394241
%N Numerator of Hermite(n, 21/22).
%H Robert Israel, <a href="/A159857/b159857.txt">Table of n, a(n) for n = 0..435</a>
%F a(n) = 21*a(n-1) + 242*(1-n)*a(n-2). - _Robert Israel_, Dec 07 2017
%F From _G. C. Greubel_, Jun 02 2018: (Start)
%F a(n) = 11^n * Hermite(n, 21/22).
%F E.g.f.: exp(21*x - 121*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(21/11)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 21/11, 199/121, -5985/1331, -270159/14641
%p f:= gfun:-rectoproc({a(n) = 21*a(n-1)+242*(1-n)*a(n-2), a(0)=1, a(1)=21}, a(n), remember): map(f, [$0..40]); # _Robert Israel_, Dec 07 2017
%t Numerator[Table[HermiteH[n,21/22],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)
%t Table[11^n*HermiteH[n, 21/22], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 21/22)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(21/22)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018
%Y Cf. A001020 (denominators), A159850
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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