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.

A160314 Numerator of Hermite(n, 16/31).

This page as a plain text file.
%I A160314 #13 Sep 08 2022 08:45:45
%S A160314 1,32,-898,-151744,322060,1176913792,34566244744,-12466050017536,
%T A160314 -863967857346928,164031013634531840,20193908432692179424,
%U A160314 -2506471012209552223232,-507146684474683728525632,41580553522411233163802624,14002144771001607102183125120
%N A160314 Numerator of Hermite(n, 16/31).
%H A160314 G. C. Greubel, <a href="/A160314/b160314.txt">Table of n, a(n) for n = 0..368</a>
%F A160314 From _G. C. Greubel_, Oct 04 2018: (Start)
%F A160314 a(n) = 31^n * Hermite(n, 16/31).
%F A160314 a(n+2) = 32*a(n+1) - 1922*(n+1)*a(n)
%F A160314 E.g.f.: exp(32*x - 961*x^2).
%F A160314 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160314 Numerators of 1, 32/31, -898/961, -151744/29791, 322060/923521, ...
%t A160314 Table[31^n*HermiteH[n, 16/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o A160314 (PARI) a(n)=numerator(polhermite(n, 16/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160314 (PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o A160314 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/31)^(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 A160314 Cf. A009975 (denominators).
%K A160314 sign,frac
%O A160314 0,2
%A A160314 _N. J. A. Sloane_, Nov 12 2009