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.

A160226 Numerator of Hermite(n, 3/29).

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%I A160226 #13 Sep 08 2022 08:45:45
%S A160226 1,6,-1646,-30060,8125356,250995816,-66828269064,-2934019389456,
%T A160226 769231923622800,44095556446256736,-11380059521124405984,
%U A160226 -809967616552784735424,205694055560527051103424,17582550705864569406418560,-4392210914651297082988957824
%N A160226 Numerator of Hermite(n, 3/29).
%H A160226 G. C. Greubel, <a href="/A160226/b160226.txt">Table of n, a(n) for n = 0..371</a>
%F A160226 From _G. C. Greubel_, Sep 26 2018: (Start)
%F A160226 a(n) = 29^n * Hermite(n, 3/29).
%F A160226 E.g.f.: exp(6*x - 841*x^2).
%F A160226 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A160226 Numerators of 1, 6/29, -1646/841, -30060/24389, 8125356/707281
%t A160226 HermiteH[Range[0,20],3/29]//Numerator (* _Harvey P. Dale_, Mar 31 2018 *)
%t A160226 Table[29^n*HermiteH[n, 3/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%o A160226 (PARI) a(n)=numerator(polhermite(n, 3/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A160226 (PARI) x='x+O('x^30); Vec(serlaplace(exp(6*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o A160226 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018
%Y A160226 Cf. A009973 (denominators).
%K A160226 sign,frac
%O A160226 0,2
%A A160226 _N. J. A. Sloane_, Nov 12 2009