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Numerator of Hermite(n, 15/22).
1

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

%S 1,15,-17,-7515,-100383,5768775,207995055,-5256335475,-431188655295,

%T 3708435650175,994755425985135,5946917116353525,-2558835187227126495,

%U -55652375114297534025,7215309872302076942895,296779894971771199420125,-21739876411879971311406975

%N Numerator of Hermite(n, 15/22).

%H G. C. Greubel, <a href="/A159840/b159840.txt">Table of n, a(n) for n = 0..434</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(-x*(121*x-15)). - _Simon Plouffe_, Jun 22 2018

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

%F a(n) = 11^n * Hermite(n, 15/22).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

%F D-finite with recurrence a(n) -15*a(n-1) +242*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 06 2021

%t Numerator[Table[HermiteH[n,15/22],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)

%t Table[11^n*HermiteH[n, 15/22], {n,0,30}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 15/22)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(15/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018

%Y Cf. A159657.

%K sign,frac

%O 0,2

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