cp's OEIS Frontend

A159884 Numerator of Hermite(n, 15/23).

%I A159884 #22 Sep 08 2022 08:45:44
%S A159884 1,30,-158,-68220,-1545108,242353800,15444235320,-1075134862800,
%T A159884 -146634052663920,4700919898821600,1537277046430494240,
%U A159884 -3617421136617700800,-17999352900456622989120,-494053808263200360316800,232741485544984381782852480,14300169574344055190498016000
%N A159884 Numerator of Hermite(n, 15/23).
%H A159884 G. C. Greubel, <a href="/A159884/b159884.txt">Table of n, a(n) for n = 0..385</a>
%H A159884 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%H A159884 Simon Plouffe, <a href="http://vixra.org/abs/1409.0048"> Conjectures of the OEIS, as of June 20, 2018.</a>
%F A159884 E.g.f.: exp(-x*(529*x-30)). - _Simon Plouffe_, Jun 22 2018
%F A159884 From _G. C. Greubel_, Jun 02 2018: (Start)
%F A159884 a(n) = 23^n * Hermite(n, 15/23).
%F A159884 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%F A159884 D-finite with recurrence a(n) -30*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 06 2021
%e A159884 Numerators of 1, 30/23, -158/529, -68220/12167, -1545108/279841, ...
%t A159884 Numerator[HermiteH[Range[0,20],15/23 ]] (* _Harvey P. Dale_, Nov 16 2014 *)
%t A159884 Table[23^n*HermiteH[n, 15/23], {n,0,30}] (* _G. C. Greubel_, Jul 16 2018 *)
%o A159884 (PARI) a(n)=numerator(polhermite(n, 15/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159884 (PARI) x='x+O('x^30); Vec(serlaplace(exp(30*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018
%o A159884 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(30/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018
%Y A159884 Cf. A009967 (denominators).
%K A159884 sign,frac
%O A159884 0,2
%A A159884 _N. J. A. Sloane_, Nov 12 2009