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A159670 Numerator of Hermite(n, 13/20). 1

%I

%S 1,13,-31,-5603,-54239,3777293,103343809,-3189282083,-186141999679,

%T 2683005336973,369934668802849,-556859979508963,-821095451099884319,

%U -9337776913476984947,2013457072984498425089,52320717306534037377757,-5360201893968552789356159

%N Numerator of Hermite(n, 13/20).

%H Vincenzo Librandi, <a href="/A159670/b159670.txt">Table of n, a(n) for n = 0..200</a>

%F Conjecture: a(n) -13*a(n-1) +200*(n-1)*a(n-2)=0. - _R. J. Mathar_, Feb 17 2014

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

%F a(n) = 10^n * Hermite(n, 13/20).

%F E.g.f.: exp(13*x - 100*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerator of 1, 13/10, -31/100, -5603/1000, -54239/10000, 3777293/100000,...

%p A159670 := proc(n)

%p orthopoly[H](n,13/20) ;

%p numer(%) ;

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

%t Numerator[Table[HermiteH[n, 13/20], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 17 2011 *)

%t Table[10^n*HermiteH[n, 13/20], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,13/20)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(13/10)^(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. A011557 (denominators).

%K sign,frac

%O 0,2

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

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Last modified November 14 07:19 EST 2019. Contains 329111 sequences. (Running on oeis4.)