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A160261 Numerator of Hermite(n, 13/29).

%I A160261 #21 Sep 08 2022 08:45:45
%S A160261 1,26,-1006,-113620,2122156,819611416,3462564856,-8181491724016,
%T A160261 -253487023438960,103499490028946336,6528273301571581216,
%U A160261 -1571126316446016259904,-161635396853273818415936,27509093252961272911088000,4249556012170678409171144576
%N A160261 Numerator of Hermite(n, 13/29).
%H A160261 Vincenzo Librandi, <a href="/A160261/b160261.txt">Table of n, a(n) for n = 0..200</a>
%H A160261 DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F A160261 D-finite with recurrence a(n) -26*a(n-1) +1682*(n-1)*a(n-2)=0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F A160261 From _G. C. Greubel_, Jul 12 2018: (Start)
%F A160261 a(n) = 29^n * Hermite(n, 13/29).
%F A160261 E.g.f.: exp(26*x - 841*x^2).
%F A160261 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160261 Numerator of 1, 26/29, -1006/841, -113620/24389, 2122156/707281, 819611416/20511149,...
%p A160261 A160261 := proc(n)
%p A160261         orthopoly[H](n,13/29) ;
%p A160261         numer(%) ;
%p A160261 end proc: # _R. J. Mathar_, Feb 16 2014
%t A160261 Numerator[HermiteH[Range[0,20],13/29]] (* _Harvey P. Dale_, May 15 2012 *)
%t A160261 Table[29^n*HermiteH[n, 13/29], {n,0,30}] (* _G. C. Greubel_, Jul 12 2018 *)
%o A160261 (PARI) a(n)=numerator(polhermite(n,13/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160261 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 12 2018
%Y A160261 Cf. A009973 (denominators).
%K A160261 sign,frac
%O A160261 0,2
%A A160261 _N. J. A. Sloane_, Nov 12 2009