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A159519 Numerator of Hermite(n, 13/15).

%I A159519 #21 Sep 08 2022 08:45:43
%S A159519 1,26,226,-17524,-760724,11764376,2017502776,20691256976,
%T A159519 -5817161063024,-225734712752224,17690399773689376,
%U A159519 1475756601500931776,-49197807240738185024,-9248228636364224401024,47353227812848547963776,59495024332228675973509376
%N A159519 Numerator of Hermite(n, 13/15).
%H A159519 Vincenzo Librandi, <a href="/A159519/b159519.txt">Table of n, a(n) for n = 0..200</a>
%H A159519 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A159519 D-finite with recurrence a(n) -26*a(n-1) + 450*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A159519 From _G. C. Greubel_, Jun 11 2018: (Start)
%F A159519 a(n) = 15^n * Hermite(n,13/15).
%F A159519 E.g.f.: exp(26*x-225*x^2).
%F A159519 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159519 Numerator of 1, 26/15, 226/225, -17524/3375, -760724/50625, 11764376/759375, ...
%p A159519 A159519 := proc(n)
%p A159519         orthopoly[H](n,13/15) ;
%p A159519         numer(%) ;
%p A159519 end proc: # _R. J. Mathar_, Feb 16 2014
%t A159519 Numerator[Table[HermiteH[n,13/15],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011 *)
%o A159519 (PARI) a(n)=numerator(polhermite(n,13/15)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159519 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 11 2018
%Y A159519 Cf. A001024 (denominators).
%K A159519 sign,frac
%O A159519 0,2
%A A159519 _N. J. A. Sloane_, Nov 12 2009