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.

A160306 Numerator of Hermite(n, 8/31).

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%I A160306 #18 Sep 08 2022 08:45:45
%S A160306 1,16,-1666,-88160,8195596,808903616,-65817219704,-10381352014976,
%T A160306 719403241658000,171134120448798976,-9706091347019300384,
%U A160306 -3444495256578225124864,150094259153430446720704,81845346744175071427394560,-2440729611300811998925197184
%N A160306 Numerator of Hermite(n, 8/31).
%H A160306 G. C. Greubel, <a href="/A160306/b160306.txt">Table of n, a(n) for n = 0..368</a>
%F A160306 a(n+2) = 16*a(n+1) - 1922*(n+1)*a(n). - _Bruno Berselli_, Mar 28 2018
%F A160306 From _G. C. Greubel_, Oct 04 2018: (Start)
%F A160306 a(n) = 31^n * Hermite(n, 8/31).
%F A160306 E.g.f.: exp(16*x - 961*x^2).
%F A160306 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160306 Numerators of 1, 16/31, -1666/961, -88160/29791, 8195596/923521, ...
%t A160306 Table[31^n*HermiteH[n, 8/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o A160306 (PARI) a(n)=numerator(polhermite(n, 8/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160306 (PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o A160306 (Maxima) makelist(num(hermite(n, 8/31)), n, 0, 20); /* _Bruno Berselli_, Mar 28 2018 */
%o A160306 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018
%Y A160306 Cf. A009975 (denominators).
%K A160306 sign,frac
%O A160306 0,2
%A A160306 _N. J. A. Sloane_, Nov 12 2009