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.

A160301 Numerator of Hermite(n, 3/31).

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%I A160301 #20 Sep 08 2022 08:45:45
%S A160301 1,6,-1886,-34380,10668396,328323816,-100553342664,-4389550302096,
%T A160301 1326507370388880,75452769667361376,-22493207874982677984,
%U A160301 -1585161480256581714624,466040432011344287649984,39356406972705866391987840,-11408347792399213172870573184
%N A160301 Numerator of Hermite(n, 3/31).
%H A160301 G. C. Greubel, <a href="/A160301/b160301.txt">Table of n, a(n) for n = 0..368</a>
%F A160301 a(n+2) = 6*a(n+1) - 1922*(n+1)*a(n). - _Bruno Berselli_, Mar 28 2018
%F A160301 From _G. C. Greubel_, Oct 04 2018: (Start)
%F A160301 a(n) = 31^n * Hermite(n, 3/31).
%F A160301 E.g.f.: exp(6*x - 961*x^2).
%F A160301 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160301 Numerators of 1, 6/31, -1886/961, -34380/29791, 10668396/923521, ...
%t A160301 Table[31^n*HermiteH[n, 3/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o A160301 (PARI) a(n)=numerator(polhermite(n, 3/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160301 (PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o A160301 (Maxima) makelist(num(hermite(n, 3/31)), n, 0, 20); /* _Bruno Berselli_, Mar 28 2018 */
%o A160301 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/31)^(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 A160301 Cf. A009975 (denominators).
%K A160301 sign,frac
%O A160301 0,2
%A A160301 _N. J. A. Sloane_, Nov 12 2009