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.

A160270 Numerator of Hermite(n, 16/29).

This page as a plain text file.
%I A160270 #19 Sep 08 2022 08:45:45
%S A160270 1,32,-658,-128704,-798260,840376192,33605404744,-7405703577856,
%T A160270 -632652549947248,79406265745318400,12118094804951629024,
%U A160270 -947834356077803359232,-254539689475704747697472,10985818579851831076419584,5917311044631018607598349440
%N A160270 Numerator of Hermite(n, 16/29).
%H A160270 G. C. Greubel, <a href="/A160270/b160270.txt">Table of n, a(n) for n = 0..371</a>
%F A160270 From _G. C. Greubel_, Oct 03 2018: (Start)
%F A160270 a(n) = 29^n * Hermite(n, 16/29).
%F A160270 E.g.f.: exp(32*x - 841*x^2).
%F A160270 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160270 Numerators of 1, 32/29, -658/841, -128704/24389, -798260/707281, ...
%t A160270 Numerator/@HermiteH[Range[0,20],16/29] (* _Harvey P. Dale_, Jun 07 2011 *)
%t A160270 Table[29^n*HermiteH[n, 16/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)
%o A160270 (PARI) a(n)=numerator(polhermite(n, 16/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160270 (PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018
%o A160270 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018
%Y A160270 Cf. A009973 (denominators).
%K A160270 sign,frac
%O A160270 0,2
%A A160270 _N. J. A. Sloane_, Nov 12 2009