cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A160132 Numerator of Hermite(n, 10/27).

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%I A160132 #16 Sep 08 2022 08:45:44
%S A160132 1,20,-1058,-79480,3038092,524289200,-11661906680,-4819720055200,
%T A160132 22627018472080,56669755093294400,836483365475254240,
%U A160132 -809515361950727267200,-29605827454506672845120,13571164223599790810028800,832572138044715293306980480
%N A160132 Numerator of Hermite(n, 10/27).
%H A160132 G. C. Greubel, <a href="/A160132/b160132.txt">Table of n, a(n) for n = 0..375</a>
%F A160132 From _G. C. Greubel_, Sep 24 2018: (Start)
%F A160132 a(n) = 27^n * Hermite(n, 10/27).
%F A160132 E.g.f.: exp(20*x - 729*x^2).
%F A160132 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160132 Numerators of 1, 20/27, -1058/729, -79480/19683, 3038092/531441, ...
%t A160132 Numerator/@(HermiteH[#,10/27]&/@Range[0,20])  (* _Harvey P. Dale_, Mar 30 2011 *)
%t A160132 Table[27^n*HermiteH[n, 10/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o A160132 (PARI) a(n)=numerator(polhermite(n, 10/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160132 (PARI) x='x+O('x^30); Vec(serlaplace(exp(20*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o A160132 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/27)^(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 A160132 Cf. A009971 (denominators).
%K A160132 sign,frac
%O A160132 0,2
%A A160132 _N. J. A. Sloane_, Nov 12 2009