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%I #13 Sep 08 2022 08:45:45
%S 1,36,-386,-135000,-2912244,803439216,53415783816,-6185340350496,
%T -851589691267440,52572710870646336,14783982337749774816,
%U -352049632685279478144,-286207027989716394858816,-3197683221510109228058880,6143086278048774757772750976
%N Numerator of Hermite(n, 18/29).
%H G. C. Greubel, <a href="/A160280/b160280.txt">Table of n, a(n) for n = 0..371</a>
%F From _G. C. Greubel_, Oct 03 2018: (Start)
%F a(n) = 29^n * Hermite(n, 18/29).
%F E.g.f.: exp(36*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 36/29, -386/841, -135000/24389, -2912244/707281, ...
%t Table[29^n*HermiteH[n, 18/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 18/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018
%Y Cf. A009973 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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