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%I #13 Sep 08 2022 08:45:44
%S 1,3,-383,-3501,439905,6809283,-841785951,-18540791469,2254238275137,
%T 64906636872195,-7758232724066751,-277708714711204653,
%U 32620373362042216353,1404202914087633336771,-162020813910704234524575,-8192328034245044455772973,928105401692205765637182081
%N Numerator of Hermite(n, 3/28).
%H G. C. Greubel, <a href="/A160192/b160192.txt">Table of n, a(n) for n = 0..417</a>
%F From _G. C. Greubel_, Sep 24 2018: (Start)
%F a(n) = 14^n * Hermite(n, 3/28).
%F E.g.f.: exp(3*x - 196*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 3/14, -383/196, -3501/2744, 439905/38416, ...
%t Table[14^n*HermiteH[n, 3/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 3/28)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(3*x - 196*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018
%Y Cf. A001023 (denominators)
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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