%I #13 Sep 08 2022 08:45:44
%S 1,44,878,-54472,-5183540,2449744,27528715336,1195712499872,
%T -151266315784048,-16776228493414720,702203805185457376,
%U 208389464888487862144,996888570345112992448,-2601849549129056926112512,-128192585558205188847080320,32898121757138562880306993664
%N Numerator of Hermite(n, 22/23).
%H G. C. Greubel, <a href="/A159948/b159948.txt">Table of n, a(n) for n = 0..385</a>
%F From _G. C. Greubel_, Jul 16 2018: (Start)
%F a(n) = 23^n * Hermite(n, 22/23).
%F E.g.f.: exp(44*x - 529*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 44/23, 878/529, -54472/12167, -5183540/279841, ...
%t Numerator[Table[HermiteH[n, 22/23], {n, 0, 30}]] (* or *) Table[23^n * HermiteH[n, 22/23], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 22/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018
%Y Cf. A009967 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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