cp's OEIS Frontend

A159705 Numerator of Hermite(n, 1/21).

%I A159705 #22 Sep 08 2022 08:45:44
%S A159705 1,2,-878,-5284,2312620,23267192,-10152119816,-143434219696,
%T A159705 62392319304592,1136856492784160,-492996517654282976,
%U A159705 -11013067301664857152,4761026079678523718848,126084356480177895534464,-54337756316633597169242240,-1665565146450503848398045952
%N A159705 Numerator of Hermite(n, 1/21).
%H A159705 Vincenzo Librandi, <a href="/A159705/b159705.txt">Table of n, a(n) for n = 0..200</a>
%H A159705 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A159705 D-finite with recurrence a(n) - 2*a(n-1) + 882*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 17 2014
%F A159705 From _G. C. Greubel_, May 22 2018: (Start)
%F A159705 a(n) = 21^n * Hermite(n,1/21).
%F A159705 E.g.f.: exp(2*x-441*x^2).
%F A159705 a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/21)^(n-2k)/(k!*(n-2k)!). (End)
%e A159705 Numerator of 1, 2/21, -878/441, -5284/9261, 2312620/194481, 23267192/4084101, ...
%p A159705 A159705 := proc(n)
%p A159705         orthopoly[H](n,1/21) ;
%p A159705         numer(%) ;
%p A159705 end proc: # _R. J. Mathar_, Feb 17 2014
%t A159705 Numerator[Table[HermiteH[n, 1/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)
%o A159705 (PARI) a(n)=numerator(polhermite(n,1/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159705 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 21 2018
%Y A159705 Cf. A009965 (denominators).
%K A159705 sign,frac
%O A159705 0,2
%A A159705 _N. J. A. Sloane_, Nov 12 2009