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A158991 Numerator of Hermite(n, 4/7).

%I A158991 #22 Sep 08 2022 08:45:43
%S A158991 1,8,-34,-1840,-4724,683488,7782664,-339629632,-8055944560,
%T A158991 201822075008,8719919701984,-128026275891968,-10424283645874496,
%U A158991 67164631281958400,13817854415099775104,18392961201951276032,-20165102300581059194624,-190160981569308074375168
%N A158991 Numerator of Hermite(n, 4/7).
%H A158991 Vincenzo Librandi, <a href="/A158991/b158991.txt">Table of n, a(n) for n = 0..200</a>
%H A158991 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A158991 D-finite with recurrence a(n) -8*a(n-1) +98*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A158991 From _G. C. Greubel_, Jul 09 2018: (Start)
%F A158991 a(n) = 7^n * Hermite(n, 4/7).
%F A158991 E.g.f.: exp(8*x - 49*x^2).
%F A158991 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/7)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A158991 Numerator of 1, 8/7, -34/49, -1840/343, -4724/2401, 683488/16807, 7782664/117649...
%p A158991 A158991 := proc(n)
%p A158991         orthopoly[H](n,4/7) ;
%p A158991         numer(%) ;
%p A158991 end proc: # _R. J. Mathar_, Feb 16 2014
%t A158991 Numerator[Table[HermiteH[n,4/7],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 23 2011*)
%t A158991 Table[7^n*HermiteH[n, 4/7], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)
%o A158991 (PARI) a(n)=numerator(polhermite(n,4/7)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A158991 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 09 2018
%Y A158991 Cf. A000420 (denominators)
%K A158991 sign,frac
%O A158991 0,2
%A A158991 _N. J. A. Sloane_, Nov 12 2009