A159709 - OEIS

%I #23 Sep 08 2022 08:45:44

%S 1,10,-782,-25460,1814572,107968600,-6922576520,-640595596400,

%T 36334031470480,4883382842903200,-239585713383638240,

%U -45467293808242606400,1869787653165632140480,499923714198096067542400,-16439748089216177447319680,-6337455503810252016486752000

%N Numerator of Hermite(n, 5/21).

%H Vincenzo Librandi, <a href="/A159709/b159709.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) - 10*a(n-1) + 882*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 17 2014

%F From _G. C. Greubel_, May 22 2018: (Start)

%F a(n) = 21^n * Hermite(n,5/21).

%F E.g.f.: exp(10*x-441*x^2).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/21)^(n-2k)/(k!*(n-2k)!). (End)

%e Numerator of 1, 10/21, -782/441, -25460/9261, 1814572/194481, 107968600/4084101, ...

%p A159709 := proc(n)

%p         orthopoly[H](n,5/21) ;

%p         numer(%) ;

%p end proc: # _R. J. Mathar_, Feb 17 2014

%t Numerator[Table[HermiteH[n, 5/21], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,5/21)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/21)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, May 22 2018

%Y Cf. A009965 (denominators).

%K sign,frac

%O 0,2

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