cp's OEIS Frontend

A160193 Numerator of Hermite(n, 5/28).

%I A160193 #22 Sep 08 2022 08:45:44
%S A160193 1,5,-367,-5755,402817,11037925,-734331695,-29632858075,1866841880705,
%T A160193 102262852326725,-6074903893493615,-431244900588230075,
%U A160193 24038761085803317505,2148769817796050860325,-111757677404273451703855,-12351237147086094379982875,595378957401697424118753025
%N A160193 Numerator of Hermite(n, 5/28).
%H A160193 G. C. Greubel, <a href="/A160193/b160193.txt">Table of n, a(n) for n = 0..417</a>
%H A160193 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A160193 D-finite with recurrence a(n) -5*a(n-1) +392*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A160193 From _G. C. Greubel_, Jul 09 2018: (Start)
%F A160193 a(n) = 14^n * Hermite(n, 5/28).
%F A160193 E.g.f.: exp(5*x - 196*x^2).
%F A160193 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160193 Numerator of 1, 5/14, -367/196, -5755/2744, 402817/38416, 11037925/537824,..
%p A160193 A160193 := proc(n)
%p A160193         orthopoly[H](n,5/28) ;
%p A160193         numer(%) ;
%p A160193 end proc: # _R. J. Mathar_, Feb 16 2014
%t A160193 Numerator/@HermiteH[Range[0,20],5/28] (* _Harvey P. Dale_, Jul 11 2011 *)
%t A160193 Table[14^n*HermiteH[n, 5/28], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)
%o A160193 (PARI) a(n)=numerator(polhermite(n,5/28)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160193 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/14)^(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 A160193 Cf. A001023 (denominators).
%K A160193 sign,frac
%O A160193 0,2
%A A160193 _N. J. A. Sloane_, Nov 12 2009