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A159527 Numerator of Hermite(n, 13/16). 1


%S 1,13,41,-2795,-52079,754013,43132729,-18356507,-38885559775,

%T -486715213907,38468867080009,1123090745841077,-39563985152718671,

%U -2239399192597236995,36722281790359787609,4490393016408925933957,-12131671824174755067839

%N Numerator of Hermite(n, 13/16).

%H G. C. Greubel, <a href="/A159527/b159527.txt">Table of n, a(n) for n = 0..450</a>

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

%F a(n) = 16^n * Hermite(n,13/16).

%F E.g.f.: exp(26*x-252*x^2).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/8)^(n-2k)/(k!*(n-2k)!). (End)

%t Numerator[Table[HermiteH[n,13/16],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,13/16)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(13/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y Cf. A159521.

%K sign,frac

%O 0,2

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

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Last modified December 11 17:59 EST 2019. Contains 329925 sequences. (Running on oeis4.)