%I #17 Sep 08 2022 08:45:44
%S 1,42,514,-83412,-5430804,188966232,41879106744,341675743248,
%T -352091802793584,-18204613149810528,3196439029135777824,
%U 361808103596334268608,-28755096299570905798464,-6634835598526992072655488,188607219729893552173509504,124031126202877890462758439168
%N Numerator of Hermite(n, 21/25).
%H G. C. Greubel, <a href="/A160065/b160065.txt">Table of n, a(n) for n = 0..380</a>
%F From _G. C. Greubel_, Sep 23 2018: (Start)
%F a(n) = 25^n * Hermite(n, 21/25).
%F E.g.f.: exp(42*x - 625*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 42/25, 514/625, -83412/15625, -5430804/390625, ...
%t Table[25^n*HermiteH[n, 21/25], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 21/25)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(42*x - 625*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(42/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018
%Y Cf. A009969 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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