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.

A160310 Numerator of Hermite(n, 12/31).

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%I A160310 #16 Sep 08 2022 08:45:45
%S A160310 1,24,-1346,-124560,4771596,1072135584,-20123783544,-12846838359744,
%T A160310 -37578736832880,196631096935434624,5369183316185589216,
%U A160310 -3650389283510599332096,-201124616475050111174976,79365587639487260327262720,6930073770593296325672255616
%N A160310 Numerator of Hermite(n, 12/31).
%H A160310 G. C. Greubel, <a href="/A160310/b160310.txt">Table of n, a(n) for n = 0..368</a>
%F A160310 From _G. C. Greubel_, Oct 04 2018: (Start)
%F A160310 a(n) = 31^n * Hermite(n, 12/31).
%F A160310 a(n+2) = 24*a(n+1) - 1922*(n+1)*a(n)
%F A160310 E.g.f.: exp(24*x - 961*x^2).
%F A160310 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160310 Numerators of 1, 24/31, -1346/961, -124560/29791, 4771596/923521, ...
%t A160310 Numerator/@HermiteH[Range[0,20],12/31] (* _Harvey P. Dale_, Jul 19 2011 *)
%t A160310 Table[31^n*HermiteH[n, 12/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o A160310 (PARI) a(n)=numerator(polhermite(n, 12/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160310 (PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o A160310 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/31)^(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 A160310 Cf. A009975 (denominators).
%K A160310 sign,frac
%O A160310 0,2
%A A160310 _N. J. A. Sloane_, Nov 12 2009