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%I #11 Sep 08 2022 08:45:45
%S 1,14,-1486,-67900,6547756,548499784,-47387630984,-6198886653904,
%T 471157554050960,90008424571645664,-5872265109220393184,
%U -1596153412824165573056,86302501271257396667584,33424995502240561479908480,-1419140555765946374814673024
%N Numerator of Hermite(n, 7/29).
%H G. C. Greubel, <a href="/A160246/b160246.txt">Table of n, a(n) for n = 0..371</a>
%F From _G. C. Greubel_, Sep 26 2018: (Start)
%F a(n) = 29^n * Hermite(n, 7/29).
%F E.g.f.: exp(14*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 14/29, -1486/841, -67900/24389, 6547756/707281,...
%t Table[29^n*HermiteH[n, 7/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 7/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018
%Y Cf. A009973 (denominators)
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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