A159657 - OEIS

%I #22 Sep 08 2022 08:45:44

%S 1,1,-199,-599,118801,598001,-118202999,-835804199,164648394401,

%T 1501935112801,-294865174808999,-3298735400410999,645404649179386801,

%U 8562369610165784401,-1669489718256239898199,-25644124626720436220999,4982825030141999258376001

%N Numerator of Hermite(n, 1/20).

%H Vincenzo Librandi, <a href="/A159657/b159657.txt">Table of n, a(n) for n = 0..200</a>

%H DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)

%F D-finite with recurrence a(n) -a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014

%F From _G. C. Greubel_, Jul 09 2018: (Start)

%F a(n) = 10^n * Hermite(n, 1/20).

%F E.g.f.: exp(x - 100*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 1/10, -199/100, -599/1000, 118801/10000, 598001/100000,...

%p A159657 := proc(n)

%p         orthopoly[H](n,1/20) ;

%p         numer(%) ;

%p end proc: # _R. J. Mathar_, Feb 16 2014

%t Numerator[Table[HermiteH[n, 1/20], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)

%t Table[10^n*HermiteH[n, 1/20], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,1/20)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/10)^(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 Cf. A011557 (denominators).

%K sign,frac

%O 0,3

%A _N. J. A. Sloane_, Nov 12 2009