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A158987 Numerator of Hermite(n, 3/7).

%I A158987 #25 Sep 08 2022 08:45:43
%S A158987 1,6,-62,-1548,8940,660456,-417864,-390855312,-2058477168,
%T A158987 294079701600,3580055071776,-266717777137344,-5459606030198592,
%U A158987 280902469732324992,8640952900866956160,-333552471067548152064,-14703515590679714467584,434789181089837215630848
%N A158987 Numerator of Hermite(n, 3/7).
%H A158987 Vincenzo Librandi, <a href="/A158987/b158987.txt">Table of n, a(n) for n = 0..200</a>
%H A158987 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A158987 D-finite with recurrence a(n) - 6*a(n-1) + 98*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A158987 From _G. C. Greubel_, Jul 09 2018: (Start)
%F A158987 a(n) = 7^n * Hermite(n, 3/7).
%F A158987 E.g.f.: exp(6*x-49*x^2).
%F A158987 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/7)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A158987 Numerator of 1, 6/7, -62/49, -1548/343, 8940/2401, 660456/16807, -417864/117649, ...
%p A158987 A158987 := proc(n)
%p A158987         orthopoly[H](n,3/7) ;
%p A158987         numer(%) ;
%p A158987 end proc: # _R. J. Mathar_, Feb 16 2014
%t A158987 Numerator[Table[HermiteH[n,3/7],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 23 2011 *)
%t A158987 Table[7^n*HermiteH[n, 3/7], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)
%o A158987 (PARI) a(n)=numerator(polhermite(n,3/7)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A158987 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/7)^(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 A158987 Cf. A000420 (denominators).
%K A158987 sign,frac
%O A158987 0,2
%A A158987 _N. J. A. Sloane_, Nov 12 2009