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A158960 Numerator of Hermite(n, 1/5).

%I A158960 #28 Sep 08 2022 08:45:43
%S A158960 1,2,-46,-292,6316,71032,-1436936,-24183472,454560656,10582510112,
%T A158960 -183387274976,-5658029605952,89546942024896,3573911647620992,
%U A158960 -51057689020940416,-2603853531376575232,33085559702952161536,2149253944507164508672
%N A158960 Numerator of Hermite(n, 1/5).
%C A158960 The denominators are 5^n = A000351(n) (conjectured). - _M. F. Hasler_, Feb 16 2014
%H A158960 Vincenzo Librandi, <a href="/A158960/b158960.txt">Table of n, a(n) for n = 0..200</a>
%H A158960 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A158960 D-finite with recurrence a(n) -2*a(n-1) +50*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A158960 a(n) = (-1)^floor(n/2)*2^ceiling(n/2)*A237987(n). - _M. F. Hasler_, Feb 16 2014
%F A158960 From _G. C. Greubel_, Jun 09 2018: (Start)
%F A158960 a(n) = 5^n * Hermite(n,1/5).
%F A158960 E.g.f.: exp(2*x-25*x^2).
%F A158960 a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/5)^(n-2k)/(k!*(n-2k)!). (End)
%e A158960 Numerators of 1, 2/5, -46/25, -292/125, 6316/625, 71032/3125, -1436936/15625,..
%p A158960 A158960 := proc(n)
%p A158960     orthopoly[H](n,1/5) ;
%p A158960     numer(%) ;
%p A158960 end proc: # _R. J. Mathar_, Feb 16 2014
%t A158960 Numerator[Table[HermiteH[n,1/5],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 23 2011*)
%o A158960 (PARI) A158960 = n->numerator(polhermite(n,1/5)) \\ _M. F. Hasler_, Feb 16 2014
%o A158960 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 02 2018
%K A158960 sign,frac
%O A158960 0,2
%A A158960 _N. J. A. Sloane_, Nov 12 2009