A159883 - OEIS

%I #28 Sep 08 2022 08:45:44

%S 1,28,-274,-66920,-1004084,255091088,12454154824,-1270601891552,

%T -127812323590000,7175629349576128,1417946567012111584,

%U -36215654642176309888,-17516100476867891291456,-30656862015230525822720,240058053822414522099649664,7175714947197201167276319232

%N Numerator of Hermite(n, 14/23).

%H Vincenzo Librandi, <a href="/A159883/b159883.txt">Table of n, a(n) for n = 0..390</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)

%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048"> Conjectures of the OEIS, as of June 20, 2018.</a>

%F E.g.f.: exp(-529*x^2 + 28*x). - _Simon Plouffe_, Jun 22 2018; corrected by _G. C. Greubel_, Jul 11 2018

%F From _G. C. Greubel_, Jul 11 2018: (Start)

%F a(n) = 23^n * Hermite(n, 14/23).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%F D-finite with recurrence a(n) -28*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 06 2021

%e Numerators of 1, 28/23, -274/529, -66920/12167, -1004084/279841, ...

%t Numerator[Table[HermiteH[n, 14/23], {n, 0, 40}]] (* _Vincenzo Librandi_, Jun 23 2018 *)

%t Table[23^n*HermiteH[n, 14/23], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 14/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^99); Vec(serlaplace(exp(-529*x^2+28*x))) \\ _Altug Alkan_, Jul 30 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..20]]; // _Vincenzo Librandi_, Jun 23 2018

%o (GAP) List(List([0..20],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(28/23)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # _Muniru A Asiru_, Jul 12 2018

%Y Cf. A009967 (denominators).

%K sign,frac

%O 0,2

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